Lesson: 1 Understand Area<\/strong><\/p>\n Lesson: 2 Measure Area Using Standard Units<\/strong><\/p>\n Lesson: 3 Find Area by Multiplying<\/strong><\/p>\n Lesson: 4 Area and the Distributive Property<\/strong><\/p>\n Lesson: 5 Find Areas of More Shapes<\/strong><\/p>\n Performance Task<\/strong><\/p>\n Explore and Grow<\/strong><\/p>\n Try to cover the rectangle with the given number of color tiles. Precision<\/strong> Answer: Example<\/strong> Answer: Explanation: Show and Grow<\/strong><\/p>\n Question 1. Explanation: Question 2. Answer: Explanation: Apply and Grow: Practice<\/strong><\/p>\n Find the area of the shape.<\/strong> Answer: Explanation: Question 4. Answer: Explanation: Question 5. Answer: Explanation:<\/p>\n In the above grid there are 11 color boxes Question 6. Explanation: Question 7. Explanation: Question 8. Question 9. Think and Grow: Modeling Real Life<\/strong><\/p>\n Part of a zoo map is shown. What is the area of the lion exhibit? Answer: Explanation: Show and Grow<\/strong><\/p>\n Use the field day map to answer the question. Question 10. Answer: Explanation: Question 11. Answer: Explanation: Find the area of the shape.<\/strong> Answer: Explanation: Question 2. Answer: Explanation: Question 3. Answer: Explanation: Question 4. Answer: Explanation: Question 5. Answer: Explanation: Question 6. Answer: Explanation: Question 7. Answer: Explanation: Question 8. Answer: Explanation: Modeling Real Life<\/strong> Question 9. Answer: Explanation: Question 10. Answer: Explanation: Review & Refresh<\/strong><\/p>\n Find the quotient. Question 12 Question 13. Question 14. Explore and Grow<\/strong><\/p>\n Use the colored squares. Find the area of the rectangle using the blue squares. Reasoning<\/strong> Answer: Think and Grow: Measuring Area Using Standard Units<\/strong><\/p>\n You can measure area using different standard units. Here are some standard units of length and area. Example<\/strong> Answer: Show and Grow<\/strong><\/p>\n Question 1. Answer: Apply and Grow: Practice<\/strong><\/p>\n Find the area of the shape. There are 14 color tiles in the above grid. <\/p>\n Question 3. Answer: Question 4. Answer: Question 5. Answer: Question 6. Answer: Question 7. Think and Grow: Modeling Real Life<\/strong><\/p>\n Whose puzzle has a greater area? Answer: Show and Grow<\/strong><\/p>\n Question 8. Answer: Question 9. Answer: Find the area of the shape.<\/strong> Answer: Explanation: Question 2. Answer: Explanation: Question 3. Answer: Explanation: Question 4. Answer: Explanation: Question 5. Answer: Explanation: Question 6. Answer: Question 7. Answer: Explanation: <\/p>\n Question 8. Answer: Review & Refresh<\/strong><\/p>\n Question 9. Answer: Explore and Grow<\/strong><\/p>\n Write an equation for the array. Answer: 2×3=6<\/p>\n Cover the rectangle with color tiles. Find the area of the rectangle. Structure<\/strong> Answer: Think and Grow: Find Area by Multiplying<\/strong><\/p>\n Example<\/strong> Another Way:<\/strong> Show and Grow<\/strong><\/p>\n Question 1. Answer: Question 2. Answer: Apply and Grow: Practice<\/strong><\/p>\n Find the area of the rectangle<\/strong> Answer: Question 4. Answer: Question 5. Answer: Question 6. Answer: Question 7. Answer:<\/p>\n Question 8. Answer: Think and Grow: Modeling Real Life<\/strong><\/p>\n Space Poster Your rectangular animal poster is 4 feet long and 1 foot wide. Which poster has a greater area, your animal poster or your space poster? Solve: Show and Grow<\/strong><\/p>\n Question 9. Answer: Question 10. Answer: <\/p>\n Question 11. Answer: <\/p>\n Find the area of the rectangle<\/strong> Answer: Question 2. Answer: Question 3. Answer: Question 4. Answer: Question 5. Answer: Question 6. Answer: Question 7. Answer: Question 8. Answer: Review & Refresh<\/strong><\/p>\n Use the Distributive Property to fill in the blanks<\/strong> Answer: Question 10. Answer: Explore and Grow<\/strong><\/p>\n Find the area of the rectangle two different ways. Structure<\/strong> Answer: Think and Grow: Area and the Distributive Property<\/strong><\/p>\n You can use the Distributive Property to find the area of a rectangle. First, break apart the large rectangle into smaller rectangles. Then find the sum of the areas of the smaller rectangles. Example<\/strong> Show and Grow<\/strong><\/p>\n The area\u00a0 of\u00a0 large rectangle=sum of area of smaller rectangles Therefore Question 1. Answer: Apply and Grow: Practice<\/strong><\/p>\n Use the Distributive Property to find the area of the rectangle.<\/strong> Answer: Question 3. Answer: Question 4. Answer: Question 5. Explanation: Think and Grow: Modeling Real Life<\/strong><\/p>\n Descartes cuts 1 rectangular piece of construction paper into2 rectangles. One rectangle is 8 inches wide and 10 inches long. The other rectangle is 8 inches wide and2 inches long. What were the dimensions and total area of the paper before it was cut? The piece of paper was _____ inches wide and ____ inches long before it was cut. Show and Grow<\/strong><\/p>\n Question 6. The piece of paper was 3 feet wide and 15 long before it was cut. Area of rectangle 1: 3×6=18 square feet Use the Distributive Property to find the area of the rectangle.<\/strong> Answer: Question 2. Answer: Structure<\/strong> 6x(4+5)= (6×4)+(6×5) <\/p>\n Question 4. <\/p>\n (7+1)x3=(7×3)+(1×3) Question 5. Answer: Question 6. Answer: Review & Refresh<\/strong><\/p>\n Write the fact family for the numbers.<\/strong> Answer: Question 8. Answer: Question 8. Answer: Explore and Grow<\/strong><\/p>\n Break apart the shape into two rectangles. Color each rectangle a different color. Find the area of each rectangle. Then find the total area of the shape. Answer: Reasoning<\/strong> Answer: Think and Grow: Find Areas of More Shapes<\/strong><\/p>\n Example<\/strong> One Way:<\/strong> Another Way:<\/strong> Answer: Show and Grow<\/strong><\/p>\n Question 1. Answer:<\/p>\n Apply and Grow: Practice<\/strong><\/p>\n Find the area of the shape<\/strong> Answer:<\/p>\n Question 3. Answer:<\/p>\n Divide the shape into two rectangles as 1st rectangle with 2 rows and 6 columns 2nd rectangle with 3 rows and 3 columns Question 4. Answer:<\/p>\n Question 5. Answer:<\/p>\n Question 6. Answer:<\/p>\n Question 7. Answer: Question 8. Answer: Think and Grow: Modeling Real Life<\/strong><\/p>\n What is the area of the balcony?<\/p>\n Answer: Explanation: Show and Grow<\/strong><\/p>\n Find the area of the miniature golf hole.<\/strong> Answer: Question 10. Answer: Explanation: Question 11. Answer: Explanation: Find the area of the shape<\/strong> Answer:<\/p>\n Question 2. Answer:<\/p>\n Question 3. Answer:<\/p>\n Question 4. Answer:<\/p>\n Question 5. Answer:<\/p>\n Question 6. Answer: Question 7. Answer: Question 8.Modeling Real Life<\/strong> Answer: Question 9. Answer: Review & Refresh<\/strong><\/p>\n Complete the table.<\/strong>\n
\n
\n
\n
\n
\n
<\/a>Lesson 6.1 Understand Area<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-1.png\")
\nHow many color tiles do you need to completely cover the rectangle with no gaps or overlaps?
\n____ color tiles
\nAnswer:
\n6 + 10 + 8 = 24 tiles are needed to cover the rectangle<\/p>\n
\nWhy is it important to line up the tiles side to side?
\nThink and Grow: Counting to Find Area<\/p>\n
\nIt is important to line up tiles side to side with out gaps so that we can count tiles to find area of the shape.
\nArea is the amount of surface a shape covers. The area of a unit square is 1 square unit.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-2.png\")
\n12 unit squares cover the rectangle with no gaps or overlaps. So, the area of the rectangle is 12 square units.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-3.png\")
<\/p>\n
\nFind the area of the rectangle. Count the unit squares needed to cover the rectangle.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-4.1.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-4.png\")
\n___ unit squares cover the rectangle.
\nSo, the area is ___ square units.<\/p>\n
\n18 unit squares cover the rectangle.
\nSo, the area is 18 square units.<\/p>\n
\nThere are 3 rows with 6 color tiles each in the grid
\n6+6+6=18.
\n18 unit squares cover the rectangle.
\nSo, The area is 18 square units.<\/p>\n
\nFind the area of the shape.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-5.png\")
\n___ unit squares cover the shape.
\nSo, the area is ___ square units.
\nAnswer:
\n16 unit squares cover the shape.
\nSo, the area is 16 square units.<\/p>\n
\nThere are 4 color tiles in row and there are 4 such rows of color tiles in the shape.
\nSo, 4+4+4+4=16
\nTherefore 16 unit squares cover the shape.
\nSo, the area is 16 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-6.png\")
\n___ unit squares cover the shape.
\nSo, the area is ___ square units.<\/p>\n
\n10 unit squares cover the shape.
\nSo, the area is 10 square units.<\/p>\n
\nThere are 5 color tiles in a row and there are 2 such rows in the shape.
\nSo, 5\u00d72=10
\nTherefore
\n10 unit squares cover the shape.
\nSo, The area is 10 unit squares.<\/p>\n
\nQuestion 3.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-7.png\")
\n___ unit squares cover the shape.
\nSo, the area is ___ square units.<\/p>\n
\n16 unit squares cover the shape.
\nSo, the area is 16 square units.<\/p>\n
\nSo, There are 8 color tiles in a row and there are 2 such rows in the shape.
\n8\u00d72=16
\nTherefore 16 unit squares cover the shape.
\nSo, the area is 16 unit squares.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-8.png\")
\nArea = ___ square units.<\/p>\n
\nArea =10 square units.<\/p>\n
\nIn the above grid there are 10 color boxes.
\nSo, the area of the given shape is 10 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-9.png\")
\nArea = ___ square units.<\/p>\n
\nArea = 11 square units.<\/p>\n
\nso, the area of the shape is 11 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-10.png\")
\nArea = ___ square units.
\nAnswer:
\nArea =18 square units.<\/p>\n
\nThere are 2 color boxes in first row and there are 4 color boxes in the following 4 rows.
\nSo, 2+4+4+4+4=18
\nTherefore the area of the shape is 18 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-11.png\")
\nArea = square units.
\nAnswer:
\nArea = 10 square units.<\/p>\n
\nIn the above grid there are 2 color boxes in the first row ,last row and 3 color boxes each in middle two rows.
\nSo,2+3+3+2=10
\nTherefore the area of the shape is 10 square units.<\/p>\n
\nYOU BE THE TEACHER<\/strong>
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-12.png\")
\nNewton uses 4 color tiles to cover the rectangle. He says the area is 4 square units. Is he correct? Explain.
\nAnswer:
\nNo, Newton is not correct. To find the area of the shape using tiles they must be arranged side by side without any gaps or overlaps. In the above picture there are gaps between the color tiles.<\/p>\n
\nOpen-Ended<\/strong>
\nDraw a shape that has an area of 16 square units
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-13.png\")
\nAnswer:<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-14.png\")
\nThe lion exhibit is ___ square units.<\/p>\n
\nThe lion exhibit is\u00a0 50 square units.<\/p>\n
\nIn the above zoo map the area of lion exhibit is represented using yellow colored tiles.
\nThere are 10 yellow colored tiles in a row and there are 5 such rows of yellow color tiles.
\nSo,10\u00d75=50
\nTherefore the area of the lion exhibit in the zoo is 50 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-15.png\")
<\/p>\n
\nWhat is the area of the relay race section?<\/p>\n
\nArea of Relay Race section is 23 square units.<\/p>\n
\nIn the above field day map Relay Race section is represented using blue colored tiles.
\nThere are 3 tiles in first row and 10 tiles in the following two rows.
\nSo,3+10+10=23
\nTherefore the area of the Relay Race section is 23 square units.<\/p>\n
\nWhich area is greater, the ring toss section or the relay race section? Explain.<\/p>\n
\nThe ring toss section is greater than relay race section.<\/p>\n
\nThe area of ring toss section is 30 square units and the area of the relay race section is 23 square units.so the ring toss section is greater than relay race section.<\/p>\n<\/a>Understand Area Homework & practice 6.1<\/h3>\n
\nQuestion 1.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-16.png\")
\n___ unit squares cover the shape.
\nSo, the area is ___ square units.<\/p>\n
\n18 unit squares cover the shape.
\nSo, the area is 18 square units.<\/p>\n
\nIn the above grid there is 1 blue color tile in first row followed by 3 tiles in the next,5 tiles in the later and 9 tiles at the end.
\nSo,1+3+5+9=18
\n18 color tiles cover the area.
\nTherefore the area of the given shape is 18 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-17.png\")
\nArea = ___ square units.<\/p>\n
\nArea = 20 square units.<\/p>\n
\nIn the above grid there are 4 red colored tiles in a row and there are 5 such rows.
\nSo,4\u00d75=20
\n20 tiles cover the shape.
\nTherefore the area of the given shape is 20 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-18.png\")
\nArea = ___ square units.<\/p>\n
\nArea = 17 square units.<\/p>\n
\nIn the above grid there are 17 purple colored tiles.
\nTherefore the area of the given shape is 17 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-19.png\")
\nArea = ___ square units.<\/p>\n
\nArea = 14 square units.<\/p>\n
\nThere are 6 yellow colored tiles in 2 rows each followed\u00a0 by 2 more tiles in the third row.
\nSo,6+6+2=14
\n14 tiles cover the shape.
\nTherefore the area of the shape is 14 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-20.png\")
\nArea = ___ square units.<\/p>\n
\nArea = 11 square units.<\/p>\n
\nThere are 3 green colored boxes in the first and third row of the above shape and 5 boxes in the middle row.
\nSo,3+5+3=11
\n11 color tiles cover the shape.
\nTherefore the area of the shape is 11 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-21.png\")
\nArea = ___ square units.<\/p>\n
\nArea =12 square units.<\/p>\n
\nThere are 6 color tiles each in two rows.
\nSo,6+6=12
\n12 color tiles cover the shape
\nTherefore the area of the shape is 12 square units.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-22.png\")
\nArea = ___ square units.<\/p>\n
\nArea = 20 square units.<\/p>\n
\nThere are 20 color tiles in the above grid.
\nSo, the area of the shape is 20 square units.<\/p>\n
\nYour friend says each shape has an area of 8 square units. Is your friend correct? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-23.png\")
<\/p>\n
\nMy friend is incorrect.<\/p>\n
\nOne of the shape in in the above grid has gaps.<\/p>\n
\nUse the amusement park map to answer the question.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-24.png\")
\nAnswer:<\/p>\n
\nWhat is the area of the food court section?<\/p>\n
\nThe area of the food court is 51 square units.<\/p>\n
\nThere are 9 green tiles in first 2 rows each and 11 green tiles in the following 3 rows.
\nSo,9+9+11+11+11=51
\n51 green tiles cover the food court area
\nTherefore the area of the food court is 51 square units.<\/p>\n
\nWhich area is greater, the kiddie land section or the picnic tables section? Explain.<\/p>\n
\nArea of kiddie land section is greater than area of picnic tables.<\/p>\n
\nThe kiddie land section is covered with 39 color tiles and the picnic tables section is covered with 35 color tiles.<\/p>\n
\n<\/strong>Question 11.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-25.png\")
\nAnswer:6
\nExplanation:(2\u00d76=12)<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-26.png\")
\nAnswer:4
\nExplanation:(7\u00d74=28)<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-27.png\")
\nAnswer:9
\nExplanation:(6\u00d79=54)<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.1-28.png\")
\nAnswer:7
\nExplanation:(7×7=49)<\/p>\n<\/a>Lesson 6.2 Measure Area Using Standard Units<\/h3>\n
\nHow many blue squares do you think it will take to cover the rectangle?
\n___ blue squares
\nHow many red squares do you think it will take to cover the rectangle?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-29.png\")
\nAnswer:<\/p>\n
\nArea = ___ blue square units
\nFind the area of the rectangle using the red squares.
\nArea = ___ red square units
\nAnswer:<\/strong><\/p>\n
\nWhy is the number of blue squares needed to cover the rectangle different from the number of red squares needed?<\/p>\n
\nThe number of blue squares needed to cover the rectangle is different from the number of red squares as sizes of the squares are different.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-31.png\")
\nUnit squares can represent different standard units.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-32.png\")
\nEach side is 1 unit. The area is 1 square unit.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-33.png\")
\nEach Side represents 1 inch. The area is 1 square inch.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-34.png\")
\nFind the area of the rectangle
\n___ unit squares cover the rectangle.
\nEach unit square represents
\n___________________
\nSo, the area is _____<\/p>\n
\nIn the above grid there are 3 yellow colored tiles in a row and there are 4 such rows.
\nSo,3\u00d74=12
\n12 unit squares cover the rectangle.
\nEach unit square represents 1 square meter.
\nSo, the area is 12 square meters.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-35.1.png\")
\nFind the area of the shape.
\n___ unit squares cover the rectangle.
\nEach unit square represents
\n________
\nSo, the area is ____<\/p>\n
\nIn the above grid there are 7 color tiles.
\n7 unit squares cover the rectangle.
\nEach unit square represents 1 square foot.
\nSo, the area is 7 square feet.<\/p>\n
\n<\/strong>Question 2.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-35.png\")
\nArea = ____
\nAnswer:<\/p>\n
\n14 unit squares cover the rectangle.
\nEach unit square represents 1 square foot.
\nSo, the area is 14 square feet.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-36.png\")
\nArea = ___<\/p>\n
\nThere are 16 color tiles in the above grid.
\n16 unit squares cover the area.
\nEach unit square represents 1 square centimeter.
\nSo, the area is 16 square centimeters.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-37.png\")
\nArea = ____<\/p>\n
\nThere are 18 color tiles in the grid
\n18 square units cover the rectangle.
\nEach unit square represents 1 square inch.
\nSo, the area is 18 square inches.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-38.png\")
\nArea = ___<\/p>\n
\nThere are 8 color boxes in the above grid.
\n8 unit squares cover the shape.
\nEach unit square represents 1 square meter.
\nSo, the area is 8 square meters.<\/p>\n
\nNumber Sense<\/strong>
\nWhich rectangle has an area of 12 square inches?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-39.png\")
<\/p>\n
\nIn the above grid\u00a0 the green rectangle has 12 colored tiles, Yellow rectangle has 15 colored tiles and the orange rectangle also has 12 colored tiles but the unit square representation of orange rectangle is square meter. As green rectangle unit square representation is square inch, Green colored rectangle has the area of 12 square inches.<\/p>\n
\nReasoning<\/strong>
\nIs the area of a blanket more likely to be 30 square feet or 30 square centimeters? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-40.png\")
\nAnswer:
\nCentimeter is the smaller when compared to feet. usually we have blankets in bigger size so that a person fits in to it.
\nTherefore the area of the blanket will more likely be 30 square feet.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-41.png\")
<\/p>\n
\nNewton’s puzzle is covered with 48 tiles and Descartes puzzle is covered with 40 tiles.
\nArea of Newton’s puzzle is 48 square inches and area of\u00a0 Descartes’s puzzle is 40 square inches.
\n48>40.
\nTherefore Newton’s puzzle has the greater area.<\/p>\n
\nCompare the area of Newton\u2019s puzzle shown above to the area of your friend\u2019s puzzle. Whose puzzle has a greater area?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-42.png\")
<\/p>\n
\nIn the above given puzzle there are 49 colored tiles .
\nThe area of my friend’s puzzle is 49 square inches.
\nThe area of Newton’s puzzle is 48 square inches.
\n48<49
\nTherefore Area of my friend’s puzzle is greater.<\/p>\n
\nYou want to weave a rectangular rug that has an area of 12 square feet. Draw and shade a rectangle to represent the rug.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-43.png\")
<\/p>\n
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.2.png\")
<\/p>\n<\/a>Measure Area Using Standard Units\u00a0 Homework & Practice 6.2<\/h3>\n
\nQuestion 1.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-44.png\")
<\/p>\n
\nArea = 8 square centimeters<\/p>\n
\nThere are 8 colored unit squares in the rectangle.
\nEach unit square represents 1 square centimeter.
\nSo, area is 8 square centimeters.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-45.png\")
\nArea = ___<\/p>\n
\nArea = 15 square meters<\/p>\n
\nThere are 15 colored unit squares in the above rectangle.
\nEach unit square represents 1 square meter.
\nSo, area is 15 square meters.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-46.png\")
\nArea = ___<\/p>\n
\nArea = 16 square feet<\/p>\n
\nThere are 16 color unit squares in the above grid.
\nEach unit square represents 1 square foot.
\nSo, area of the shape is 16 square feet.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-47.png\")
\nArea = ___<\/p>\n
\nArea = 20 square centimeters<\/p>\n
\nThere are 20 colored unit squares in above grid.
\nEach unit square represents 1 square centimeter.
\nSo, area of the shape is 20 square centimeters.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-48.png\")
\nArea = ___<\/p>\n
\nArea = 10 square inches<\/p>\n
\nThere are 10 colored unit squares in the above grid.
\nEach unit square represents 1 square inch.
\nSo, area of the shape is 10 square inches.<\/p>\n
\nPrecision<\/strong>
\nYour friend says the area of the shape is 13. What is wrong with her answer?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-49.png\")
<\/p>\n
\nMy friend’s answer wrong as he\/she didn’t mention the units of the area.
\nThere are 13 color unit squares in the above grid.
\nEach unit square represents 1 square centimeter.
\nTherefore area is 13 square centimeters.<\/p>\n
\nNumber Sense<\/strong>
\nFind the area of the shape.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-50.png\")
<\/p>\n
\nArea = 32 square feet<\/p>\n
\nIn the above grid there are 32 color unit squares.
\nEach unit square represents 1 square foot.
\nTherefore area of the given shape is 32 square feet.<\/p>\n
\nModeling Real Life<\/strong>
\nCompare the areas of your bookmark and your friend\u2019s bookmark. Whose bookmark has a greater area?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-51.png\")
<\/p>\n
\nMy book mark has 12 colored unit squares and my friend’s book mark has 5 colored unit squares.
\nSo area of my book mark is 12 square inches and my friend’s book mark is 5 square inches.
\n12>5
\nSo, area of my book mark is greater.<\/p>\n
\nFind the product of 4 \u00d7 5.
\nNumber of jumps: ___
\nSize of jumps: ___
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-3rd-Grade-Chapter-6-Relate-Area-to-Multiplication-52.png\")
\n4 \u00d7 5 = ___<\/p>\n
\nNumber of jumps =4
\nSize of jumps=5
\n4\u00d75=20.<\/p>\n<\/a>Lesson 6.3 Find Area by Multiplying<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-1.png\")
<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-2.png\")
\nAnswer:<\/p>\n
\nHow can you use an array to find the area of rectangle?<\/p>\n
\nWe can count the number of unit squares in a row and number of unit squares in a column and note them in the form of an array.
\nThe answer of the equation will be the area of the rectangle.<\/p>\n
\nFind the area of the rectangle.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-3.png\")
\nOne Way:<\/strong>
\nCount the unit squares to find the area.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-4.png\")
\nThere are ___ unit squares<\/p>\n
\nThink of the rectangle as an array.
\nThen use repeated addition or multiplication to find the area.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-5.png\")
\n3 rows of ____ unit squares
\n7 + 7 + 7 = ____
\n3 \u00d7 7 = _____
\nSo, the area is _____.<\/p>\n
\nFind the area of the rectangle.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-6.png\")
<\/p>\n
\nThere are 5 rows of 2 unit squares in each row.
\nSo, 5 rows of 2 unit squares
\n2+2+2+2+2=10
\nArea=10 unit squares<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-7.png\")
<\/p>\n
\n6ft\u00d74ft=24ft
\nArea =24 square feet.<\/p>\n
\nQuestion 3.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-8.png\")
\n____ \u00d7 _____ = ____
\nArea = _____<\/p>\n
\nThere are 4 rows of 1 unit square in each row.so,
\n4\u00d71=4
\nArea=4 square centimeter.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-9.png\")
\n____ \u00d7 _____ = ____
\nArea = _____<\/p>\n
\nThere are 5 rows with 3 unit squares in each roe.so,
\n5\u00d73=15
\nArea =15 square inches.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-10.png\")
\n___ \u00d7 ____ = ____
\nArea = _____<\/p>\n
\n7ft\u00d76ft=42ft
\nArea=42 square feet<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-11.png\")
\n____ \u00d7 _____ = ____
\nArea = ______<\/p>\n
\n8m\u00d74m=32m
\nArea=32 square meters.<\/p>\n
\nOpen-Ended<\/strong>
\nDraw and label two different rectangles that each have an area of 12 square meters.<\/p>\n
\nDIG DEEPER!<\/strong>
\nExplain how to find the area of the rectangle.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-12.png\")
<\/p>\n
\nWe can find area of the given rectangle by counting the number of square units in a row and in a column and multiplication of both is the area of the rectangle.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-13.png\")
\nUnderstand the problem:
\nMake a plan:<\/p>\n
\nArea of my\u00a0 animal poster is
\n4ft\u00d71ft=4 square feet.
\nArea of my space poster is
\n3ft\u00d72ft=6 square feet.
\n4<6
\nSo, my space poster has a greater area.<\/p>\n
\nDescartes\u2019s rectangular tablet is 10 inches long and 7 inches wide. Whose tablet has a greater area, Newton\u2019s tablet or Descartes\u2019s?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-14.png\")
<\/p>\n
\nArea of Newton’s table is
\n9in.\u00d76in.=54 square inches.
\nArea of Descartes’s table is
\n10in.\u00d77in.=70 square inches.
\n54<70
\nTherefore Descartes’s table has greater area.<\/p>\n
\nYour friend paints a rectangular tile that is 8 inches long and 4 inches wide. You paint a square tile that is 6 inches long. Whose tile has a greater area?<\/p>\n
\nArea of rectangular tile is
\n8in.\u00d74in.=32 square inches.
\nArea of square tile is
\n6in.\u00d76in.=36 square inches.
\n32<36
\nSo, square tile has greater area.<\/p>\n
\nDIG DEEPER!<\/strong>
\nA sign has an area of 18 square feet. The sign is 6 feet long. How wide is the sign?<\/p>\n
\nThere is a sign with an area of 18 square feet and length of 6 feet.
\nWe have to find width of sign
\nArea=length \u00d7width
\n18=6\u00d7width Or 6\u00d7width=18
\nCalculate and check 6 table 6\u00d71=6,6\u00d72=12,6\u00d73=18
\nTherefore width of the sign is 3 feet.<\/p>\n<\/a>Find Area by Multiplying Homework & Practice 6.3<\/h3>\n
\nQuestion 1.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-15.png\")
\n____ \u00d7 ____ = ____
\nArea = _____<\/p>\n
\nThere are 4 rows with 4 unit squares in each row.
\n4\u00d74=16
\nArea =16 square feet.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-16.png\")
\n____ \u00d7 _____ = _____
\nArea = _____<\/p>\n
\nThere are 3 rows with 8 unit squares in each row.
\n3\u00d78=24
\nArea=24 square centimeters.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-17.png\")
\n____ \u00d7 _____ = _____
\nArea = _____<\/p>\n
\n6 in.\u00d72 in.=12
\nArea=12 square inches.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-18.png\")
\n____ \u00d7 _____ = _____
\nArea = _____<\/p>\n
\n7 m\u00d74 m=28
\nArea=28 square meters.<\/p>\n
\nDIG DEEPER!<\/strong>
\nFind the missing side length.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-19.png\")
<\/p>\n
\nGiven Area of rectangle =30 square centimeters
\nLength =10 square meters
\nWe have to find the length of the other side called breadth or width
\nArea= length \u00d7width
\n30=10\u00d7width or 10\u00d7width=30
\nCount 10 table10\u00d71=10,10\u00d72=20,10\u00d73=30
\nTherefore width or the length of the other side is 3 square meters.<\/p>\n
\nYOU BE THE TEACHER<\/strong>
\nDescartes says he only needs the length of one side of a square to find the area. Is he correct? Explain.<\/p>\n
\nYes he is correct. A square has sides with equal lengths on all sides.so length of one side is sufficient to measure the area of a square.<\/p>\n
\nModeling Real Life<\/strong>
\nA picture of your friend is 6 inches long and 4 inches wide. Which picture has a greater area, the picture of your friend or the picture of your pets?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-20.png\")
<\/p>\n
\nArea of my friend’s picture is
\n6 in.\u00d74 in.=24 square inches.
\nArea of my pets picture is
\n7 in.\u00d75 in.=35 square inches.
\n24<35
\nTherefore pets picture has greater area.<\/p>\n
\nDIG DEEPER!<\/strong>
\nA city street parking spot has an area of 72 square feet. The parking spot is 9 feet long. How wide is the parking spot?<\/p>\n
\nThe city street parking spot has an area of 72 square feet. The length of the parking spot is 9 feet
\nWe have to find the width of the parking spot.
\nArea =length \u00d7 breadth
\n72=9\u00d7width or 9\u00d7width=72
\nSo 9\u00d71=9,9\u00d72=18,———9\u00d78=72
\nTherefore Width of the parking spot is 8 feet.<\/p>\n
\nQuestion 9.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-21.png\")
<\/p>\n
\n9\u00d73= 9\u00d7(2+1)
\n= (9\u00d72)+(9\u00d71)
\n= 18+9
\n= 27<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.3-22.png\")
<\/p>\n
\n6\u00d77 = (5+1)\u00d77
\n= (5\u00d77)+(1\u00d77)
\n= 35+7
\n= 42<\/p>\n<\/a>Lesson 6.4 Area and the Distributive Property<\/strong><\/h2>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-1.png\")
<\/p>\n
\nHow does the area of the large rectangle compare to the areas of the smaller rectangles? What property does this show?<\/p>\n
\nThe area of larger rectangle is divided in two smaller rectangles so the sum of the areas of smaller rectangles will be equal to area of larger rectangle.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-2.png\")
<\/p>\n
\nUse the Distributive Property to find the area of the rectangle.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-3.png\")
\nSo, the area is _____.<\/p>\n
\n<\/span>In the above grid there are 6 rows and 9 columns in the larger rectangle and this rectangle is divided into two smaller rectangles with 5 and 4 columns each.<\/p>\n
\n6\u00d79=6\u00d7(5+4)
\n6\u00d79=(6\u00d75)+(6\u00d74)
\n6\u00d79=30+24
\n6\u00d79=54
\nSo, the area is 54 square inches.<\/p>\n
\nUse the Distributive Property to find the area of the rectangle.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-4.png\")
<\/p>\n
\nIn the above rectangle there are 4 rows and 5 columns. This is divided\u00a0 into smaller rectangles with 3 and 2 columns each.
\nTherefore
\n4\u00d75=4\u00d7(3+2)
\n4\u00d75=(4\u00d73)+(4\u00d72)
\n4\u00d75=12+8
\n4\u00d75=20
\nArea=20 square centimeters.<\/p>\n
\nQuestion 2.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-5.png\")
<\/p>\n
\nThere are 6 columns in the above large rectangle so the columns of\u00a0 smaller rectangles are 4 and
\n2 columns each.
\nTherefore
\n7\u00d76=7\u00d7(4+2)
\n7\u00d76=(7\u00d74)+(7\u00d72)
\n7\u00d76=28+14
\n7\u00d76=42
\nArea=42 square meters.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-6.png\")
<\/p>\n
\nHere we divide the rectangle using rows.
\nThere are 3 rows in the above rectangle. so, the rows of the smaller rectangles are 2 and 1 each.
\n3\u00d74=(2+1)\u00d74
\n3\u00d74=(2\u00d74)+(1\u00d74)
\n3\u00d74=8+4
\n3\u00d74=12
\nArea=12 square feet<\/p>\n
\nStructure<\/strong>
\nWhich equation represents the area of the rectangle?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-7.png\")
\n5 \u00d7 7 = 5 \u00d7 (6 + 1) = (5 \u00d7 6) + (5 \u00d7 1)
\n5 \u00d7 8 = 5 \u00d7 (6 + 2) = (5 \u00d7 6) + (5 \u00d7 2)
\n5 \u00d7 7 = 5 \u00d7 (2 + 5) = (5 \u00d7 2) + (5 \u00d7 5)<\/p>\n
\nForm the above grid we can understand that the large rectangle has 7 columns is divided into two smaller rectangles with 2 and 5 columns each. Therefore the 3rd equation represents the area of the rectangle.<\/p>\n
\nDIG DEEPER!<\/strong>Explain how to use the Distributive Property to find the area of the rectangle.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-8.png\")
<\/p>\n
\nTo find the area of the rectangle using distributive property we have to divide the length of the rectangle into two and make two small rectangles.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-9.png\")
\nDraw a picture:
\nMultiplication equation:
\nDistributive Property:<\/p>\n
\nThe total area of the piece of paper was _____ square inches.<\/p>\n
\nYou cut 1 rectangular piece of fabric into 2 rectangles. One rectangle is 3 feet wide and 6 feet long. The other rectangle is3 feet wide and 9 feet long. What were the dimensions and total area of the fabric before it was cut?
\nAnswer:<\/p>\n
\nThe total area of the piece of paper was 45 square feets.<\/p>\n
\nArea of rectangle 2: 3×9=27 square feet.
\nArea of paper is area of rectangle 1+2=18+27=45 square feet<\/p>\n<\/a>Area and the Distributive Property Homework & Practice 6.4<\/h3>\n
\nQuestion 1.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-10.png\")
<\/p>\n
\nIn the above large rectangle there are 9 rows so, using Distributive Property we will find the area of large rectangle by dividing it\u00a0 into two smaller rectangles of 5 and 4 rows each.
\n9\u00d74=(5+4)\u00d74
\n9\u00d74=(5\u00d74)+(4\u00d74)
\n9\u00d74=20+16
\n9\u00d74=36
\nTherefore Area=36 square feet.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-11.png\")
<\/p>\n
\nIn the above large rectangle there are 5 columns so, using Distributive Property we will find the area of the large rectangle by dividing it into two smaller rectangles of 3 and 2 columns each.
\n6\u00d75=6\u00d7(3+2)
\n6\u00d75=(6\u00d73)+(6\u00d72)
\n6\u00d75=18+12
\n6\u00d75=30
\nArea=30 square centimeters.<\/p>\n
\nDraw rectangle for the expression<\/strong>
\nQuestion 3.
\n6 \u00d7 (4 + 5)
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-12.png\")
\nAnswer:<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4.png\")
<\/p>\n
\n=24+30
\n=54.<\/p>\n
\n(7 + 1) \u00d7 3
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-13.png\")
\nAnswer:<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-1-1.png\")
<\/p>\n
\n= 21+3
\n=24<\/p>\n
\nWhich One Doesn’t Belong?<\/strong>
\nWhich is not a way to break apart the rectangle?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-14.png\")
\n5 \u00d7 (4 + 4)
\n5 \u00d7 (4 + 1)
\n(4 + 1) \u00d7 8
\n(2 + 3) \u00d7 8<\/p>\n
\n5\u00d7(4+1) is not a way to break apart the given rectangle as the columns given in the rectangle are 8 and the equation shows only 5 columns.<\/p>\n
\nModeling Real Life<\/strong>
\nYou cut a rectangular piece of wrapping paper into2 rectangles. One rectangle is 10 inches wide and 6 inches long. The other rectangle is 10 inches wide and 5 inches long. What werethe dimensions and the total area of the wrapping paper before it was cut?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.4-15.png\")
<\/p>\n
\nAs we know that the area of the larger rectangle is the sum of the areas of the smaller rectangles. So the areas of 2 rectangles are
\nRectangle 1: 10 in. \u00d76 in.=60 square inches.
\nRectangle 2: 10 in. \u00d75 in.=50 square inches.
\nTherefore Total Area=110(60+50) square inches.<\/p>\n
\nQuestion 7.
\n3, 8, 24
\n___ \u00d7 ____ = _____
\n___ \u00d7 ____ = _____
\n___ \u00f7 ____ = _____
\n___ \u00f7 ____ = _____<\/p>\n
\nFact family of the numbers\u00a0 3,8,24 is given below.
\n3\u00d78=24
\n8\u00d73=42
\n24\u00f73=8
\n24\u00f78=3<\/p>\n
\n4, 9, 36
\n___ \u00d7 ____ = _____
\n___ \u00d7 ____ = _____
\n___ \u00f7 ____ = _____
\n___ \u00f7 ____ = _____<\/p>\n
\nFact family of the numbers 4,9,36 is given below.
\n4\u00d79=36
\n9\u00d74=36
\n36\u00f74=9
\n36\u00f79=4<\/p>\n
\n2, 7, 14
\n___ \u00d7 ____ = _____
\n___ \u00d7 ____ = _____
\n___ \u00f7 ____ = _____
\n___ \u00f7 ____ = _____<\/p>\n
\nFact family of the numbers 2,7,14 is given below.
\n2\u00d77=14
\n7\u00d72=14
\n14\u00f72=7
\n14\u00f77=2<\/p>\n<\/a>Lesson 6.5 Find Areas of More Shapes<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-1.png\")
\nAreas of Rectangles
\nRectangle 1: _____ \u00d7 ____ = _____ square inches
\nRectangle 2: _____ \u00d7 ____ = ______ square inches
\nTotal Area of Shape: ____ + ____ = ____ square inches<\/p>\n
\nWe have broken the shape into two rectangles
\nRectangle 1:3\u00d710=30 square inches
\nRectangle 2: 5\u00d77\u00a0 =35 square inches
\nTotal Area of Shape: 30+35=75 square inches.<\/p>\n
\nBreak apart the shape into two different rectangles and find the total area. What do you notice? Why is this true?<\/p>\n
\nWhen we broke apart the shape into two rectangles we noticed that the counting of rows and columns or units squares became possible. yes it is right to break the shape to find the area.<\/p>\n
\nFind the area of the shape
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-2.png\")
<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-3.png\")
\nAreas of Rectangles
\nRectangle A: 5 \u00d7 4 = _____ square feet
\nRectangle B: 2 \u00d7 4 = ______ square feet
\nArea of Shape: ____ + ____ = ____ square feet<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-4.png\")
\nAreas of Rectangles
\nRectangle A: 3 \u00d7 4 = _____ square feet
\nRectangle B: 2 \u00d7 8 = ______ square feet
\nArea of Shape: ____ + ____ = ____ square feet<\/p>\n
\nAreas of Rectangles
\nRectangle A:3\u00d74=12 square feet
\nRectangle B:2\u00d78=16 square feet
\nArea of the shape:12+16=28 square feet.<\/p>\n
\nFind the area of the shape
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-5.png\")
\nAreas of Rectangles
\nRectangle A: _____ \u00d7 ____ = _____ square meters
\nRectangle B: _____ \u00d7 ____ = ______ square meters
\nArea of Shape: ____ + ____ = ____ square meters<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4..png\")
\nRectangle A:3\u00d74=12 square meters
\nRectangle B:4\u00d72=8 square meters
\nArea of shape:12+8=20 square meters.<\/p>\n
\nQuestion 2.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-6.png\")
\nAreas of Rectangle A: _____ \u00d7 ____ = _____ square inches
\nAreas of Rectangle B: _____ \u00d7 ____ = ______ square inches
\nArea of Shape: ____ + ____ = ____ square inches<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-q2.png\")
\nDivide the shape into two rectangles as 1st rectangle with 3 rows and 5 columns 2nd rectangle with 2 rows and 7 columns
\nArea of Rectangle A:3\u00d75=15 square inches
\nArea of Rectangle B:2\u00d77=14 square inches
\nArea of shape:15+14=29 square inches.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-7.png\")
\nArea = _____<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-q3.png\")
<\/p>\n
\nArea of Rectangle 1: 2\u00d76=12 square centimeters
\nArea of Rectangle 2: 3\u00d73=9 square centimeters
\nArea of shape: 12+9=21 square centimeters.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-8.png\")
\nArea = ____<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-q4.png\")
\nDivide the shape into two rectangles as 1st rectangle with 1 row and 6 columns 2nd rectangle with 3 rows and 4 columns
\nArea of Rectangle 1: 1\u00d76=6 square inches
\nArea of Rectangle 2: 3\u00d74=12 square inches
\nArea of shape: 6+12=18 square inches.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-9.png\")
\nArea = ____<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-q5.png\")
\nDivide the shape into two rectangles as 1st rectangle with 4 rows and 5 columns 2nd rectangle with 6 rows and 2 columns
\nArea Of Rectangle 1:4\u00d75=20 square feet
\nArea of Rectangle 2:6\u00d72=12 square feet
\nArea of shape : 20+12=32 square feet.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-10.png\")
\nArea = _____<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-q6.png\")
\nDivide the shape into two rectangles as 1st rectangle with 3 rows and 8 columns 2nd rectangle with 2 rows and 5 columns
\nArea of Rectangle 1:3\u00d78=24 square meters
\nArea of Rectangle 2:2\u00d75=10 square meters
\nArea of shape:24+10=34 square meters.<\/p>\n
\nYOU BE THE ANSWER<\/strong>
\nYour friend says there is only one way to break apart the shape. Is your friend correct? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-11.png\")
<\/p>\n
\nNo my friend is correct if we break the shape in any other way we will not get 2 rectangles.we may get 1 square and 1 rectangle.<\/p>\n
\nDIG DEEPER!<\/strong>
\nNewton uses square tiles to make the design. Each tile is 2 inches long. What is the area of the design? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-12.png\")
<\/p>\n
\nGiven: Each tile is 2 inches long and tile is square shape
\nTherefore area of each square tile is 2\u00d72=4 square inches.
\nIn the above shape we have 4 tiles
\nSo, Area of shape = 4 \u00d7 (area of tile) = 4 \u00d74=16 square inches.
\nArea=16 square inches.<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-13.png\")
<\/p>\n
\nThe area of the balcony is 46 square feet<\/p>\n
\nArea of Rectangle A:5\u00d78=40 square feet , Area of Rectangle B:3\u00d72=6 square feet
\nArea of the balcony:46 square feet<\/p>\n
\nQuestion 9.<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-14.png\")
<\/p>\n
\nArea of Rectangle A:4\u00d7(8+6)=4\u00d7(14)=56 square feet
\nArea of Rectangle B:6\u00d7(10-4)=6\u00d76=36 square feet
\nArea of the golf hole:56+36=92 square feet<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-15.png\")
<\/p>\n
\nArea=52 square feet<\/p>\n
\nTo find area here we need to calculate the total area and subtract the middle area from it. Total shape Length =6+4=10 , width =2+3+2=7 , Area of total shape =10\u00d77=70 square feet, Part to be subtracted length =3 ,width =6
\nArea =3\u00d76=18 square feet
\nTherefore area of the shape =Total area-area of part to be subtracted
\n=70\u201018=52 square feet.<\/p>\n
\nDIG DEEPER!<\/strong>
\nThe floors of the classroom and closet have an area of 98 square meters. What is the area of the closet floor? Explain
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-16.png\")
<\/p>\n
\nArea of closets =8 square meters.<\/p>\n
\nGiven here that total area is 98 square meters. As shown in the figure above area of class room is 9\u00d710=90 square meters.
\nTherefore Area of closets = Total area – Area of class room
\n=98-90=8
\nArea of closets =8 square meters.<\/p>\n<\/a>Find Areas of More Shapes Homework & Practice 6.5<\/h3>\n
\nQuestion 1.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-17.png\")
\nAreas of Rectangle A: _____ \u00d7 ____ = _____ square feet
\nAreas of Rectangle B: _____ \u00d7 ____ = ______ square feet
\nArea of Shape: ____ + ____ = ____ square feet<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-Q1.png\")
\nArea of Rectangle A:4\u00d72=8 square feet
\nArea of Rectangle B:=1\u00d77=7 square feet
\nArea of shape:=8+7=15 square feet.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-18.png\")
\nArea = ____<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-Q-2.png\")
\nArea of Rectangle A: 2\u00d73=6 square meters
\nArea of Rectangle B: 3\u00d76=18 square meters
\nArea of shape: 6+18=24 square meters.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-19.png\")
\nArea = _____<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-Q-3.png\")
\nArea of Rectangle A: 3\u00d77=21 square feet
\nArea of Rectangle B: 2\u00d73=6 square feet
\nArea of shape: 21+6=27 square feet.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-20.png\")
\nArea = _____<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-Q-4.png\")
\nArea of Rectangle A:2\u00d76=12 square inches.
\nArea of Rectangle B:4\u00d78=36 square inches.
\nArea of shape :12+36=48 square inches.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-21.png\")
\nArea = _____<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-idea-math-grade3-chapter6-Relate-Area-to-Multiplication-lesson6.4-Q-5.png\")
\nArea of square A:4\u00d74=16 square centimeters
\nArea of square B:4\u00d74=16 square centimeters
\nArea of shape:16+16=32 square centimeters.<\/p>\n
\nNumber Sense<\/strong>
\nNewton makes a design with squares. What is the total area of his design?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-22.png\")
<\/p>\n
\nArea of blue square is 2\u00d72=4 square meters
\nArea of yellow square is 4\u00d74=16 square meters
\nArea of green square is 6\u00d76=36 square meters
\nTherefore Area of shape=4+16+36=56 square meters<\/p>\n
\nPrecision<\/strong>
\nA landscaper sketches a design for a yard.How much greater is the area of the grass than the area of the rocks?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-23.png\")
<\/p>\n
\nArea of rock is 3\u00d74=12 square feet.
\nTo find area of the grass we divide it into 2 rectangles with 3 rows, 7 columns and 6 rows and 3 columns.
\nArea=(3\u00d77)+(7\u00d76) =21+42=63.
\nArea of grass- area of rock=63\u201012=51.
\nSo, area of grass is 53 square feet more than area of rock.<\/p>\n
\nWhat is the area of the counter top?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-24.png\")
<\/p>\n
\nDivide the shape into 2 parts
\n1:8ft\u00d73ft=24 square feet
\n2:6ft\u00d72ft=12 square feet
\nArea of counter top = 21+12=33 square feet.<\/p>\n
\nDIG DEEPER!<\/strong>
\nThe floors of the barn stall and feeding area havean area of 22 square meters. What is the area of the barn stall floor? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-25.png\")
<\/p>\n
\nThe total area of bran stall and feeding areas 22 square meters. Feeding area =3\u00d72=6 square meters
\nThe area of only barn stall floor =Total area \u2010feeding area
\n=22\u20106 = 16 square meters
\nTherefore area of barn stall floor is 16 square meters.<\/p>\n
\nQuestion 10.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-26.png\")
\nAnswer:
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-ideas-math-answer-key-grade-3-chapter-6-relate-area-multiplication.png\")
<\/a><\/p>\n
![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-3-Chapter-6-Relate-Area-to-Multiplication-6.5-27.png\")