Area of a Square – Definition<\/h2>\n
The area of a square is defined as the total number of unit squares in the shape of a square. A Square is a rectangle whose length and breadth are equal which means all four sides are equal.<\/p>\n
![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/square-definition.jpg\")
<\/a>Area of a Square Formula<\/h3>\nThe area of a square formula is used for calculating the occupied region. It is measured in square units.
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/area-of-a-square.png\")
<\/a><\/p>\nArea of a square=side x side<\/p>\n
Perimeter of a Square Formula<\/h4>\n
The perimeter of the square is equal to the sum of all its four sides. The unit of the perimeter remains the same as that of the side-length of a square.<\/p>\n
Perimeter=side+side+side+side=4side unit<\/p>\n
Perimeter =4 x side of the square = 4a unit<\/p>\n
Where ‘a’ is the length of the side of the square.<\/p>\n
Also, Read: Perimeter of a Square<\/a><\/p>\nLength of Diagonal of a Square<\/h4>\n
The length of the diagonals of the square is equal to s\u221a2, where s is the side of the square. The length of the diagonals is equal to each other. By Pythagoras theorem, diagonal is the hypotenuse and the two sides of the triangle formed by the diagonal of the square, are perpendicular and base. Hypotenuse\u00b2=Base\u00b2 + Perpendicular\u00b2<\/p>\n
Hence,Diagonal\u00b2=side\u00b2 + side\u00b2<\/p>\n
Diagonal=\u221a2side\u00b2, d=s\u221a2<\/p>\n
where d is the length of the diagonal of a square and s is the side of the square.<\/p>\n
Diagonal of Square<\/h4>\n
It is a line segment that connects two opposite vertices of the square. Suppose we have four vertices, thus we can have two diagonals within a square. The diagonal of a square is always greater than its sides.<\/p>\n
The relation between Diagonal ‘d’ and Side ‘a’ of a square is, d=a\u221a2<\/p>\n
The relation between Diagonal ‘d’ and Area ‘A’ of a square is, d=\u221a(2A)<\/p>\n
The relation between Diagonal ‘d’ and Perimeter ‘P’ of a square is,d=p\/2\u221a2<\/p>\n
Area of Square Units<\/h4>\n
Usually, the Area of the Square is measured in the Square Units since each side of the square is the same. Some of the Common Units of Measurement and their equivalent are expressed below.<\/p>\n
\n- 1 m=100 cm<\/li>\n
- 1 sq.m=10,000 sq.cm<\/li>\n
- 1 km=1000 m<\/li>\n
- 1 sq.km=1,000,000 sq.m<\/li>\n<\/ul>\n
Properties of a Square<\/h3>\n
Have a glance at the Properties of Square and get an idea of them so that you might find them useful while solving related problems. They are as follows<\/p>\n
\n- The square has 4 vertices and 4 sides.<\/li>\n
- All four interior angles are equal to 90\u2070.<\/li>\n
- The opposite sides of the square are parallel to each other.<\/li>\n
- The two diagonals of the square are equal to each other.<\/li>\n
- The length of diagonals is greater than the sides of the square.<\/li>\n<\/ol>\n
Solved Problems on Area of a Square<\/h3>\n
1. Find the Area of a square of the Side 2.5 cm?<\/strong><\/p>\nSolution: <\/strong><\/p>\nGiven, Area of a square of the side is\u00a0 2.5 cm<\/p>\n
Area of a square = length x length<\/p>\n
Substitute the given value in the above formula,<\/p>\n
= 2.5 x\u00a0 2.5 sq. cm<\/p>\n
= 6. 25 sq. cm<\/p>\n
2. Find the area of a square of side 49 m?<\/strong><\/p>\nSolution:\u00a0 <\/strong><\/p>\nGiven, Area of a square of the side is 49 m<\/p>\n
Area of a square\u00a0 = length\u00a0 x\u00a0 length<\/p>\n
Substitute the given value in the above formula,<\/p>\n
= 49\u00a0 x\u00a0 49 sq. m.<\/p>\n
= 2401 sq. m.<\/p>\n
3. Let a square has a side equal to 3 cm. Find out its area, length of diagonal, and perimeter?<\/strong><\/p>\nSolution: <\/strong><\/p>\nGiven, side of the square, s= 3 cm<\/p>\n
Area of a square= s\u00b2<\/p>\n
Therefore, by substituting the value of the side, we get,<\/p>\n
3\u00b2 = 9 cm\u00b2<\/p>\n
Length of the diagonal of\u00a0 square = s\u221a2<\/p>\n
By substituting the value, we get,<\/p>\n
3 x 1.414 = 4.242<\/p>\n
The perimeter of the square = 4 xs<\/p>\n
substituting the value in the above formula, we get,<\/p>\n
4 x 3= 12 cm.<\/p>\n
4. Find the area of a square clipboard whose side measures 120 cm?<\/strong><\/p>\nSolution: <\/strong><\/p>\nGiven, side of the clipboard\u00a0 = 140 cm = 1.4 m<\/p>\n
Area of the clipboard\u00a0 = side x side<\/p>\n
substituting the value in the above formula, we get,<\/p>\n
Area of the clipboard\u00a0 = 140 cm x 140 cm<\/p>\n
= 19,600 sq . cm<\/p>\n
= 1.96 sq . m<\/p>\n
5. A wall that is 40 m long and 30 m wide is to be covered by square tiles. The side of each tile is\u00a0 2 m. Find the number of tiles required to cover the wall?<\/strong><\/p>\nSolution:\u00a0 <\/strong><\/p>\nGiven, Length of the wall = 40 m<\/p>\n
The breadth of the wall = 30 m<\/p>\n
Area of the wall = Length x breadth<\/p>\n
substituting the length and breadth values, we get<\/p>\n
Area of the wall= 40 m x 30 m = 1200 sq. m<\/p>\n
side of one tile = 2 m<\/p>\n
Area of one tile = side x side<\/p>\n
substitute the value in the above formula, we get<\/p>\n
Area of one tile =2 m x 2 m= 4 sq. m<\/p>\n
No. of tiles required = Area of wall\/ Area of a tile<\/p>\n
substitute the value, we get<\/p>\n
No.of tiles required = 1200\/ 4 = 300 tiles<\/p>\n
FAQ’s on Area of a Square<\/h3>\n
\u00a01. What is the Area of a Square Formula?<\/span><\/strong><\/p>\nThe area of a square can be calculated by using a formula side x side square units.<\/p>\n
2. Define Perimeter<\/strong> and Area of a Square?<\/strong><\/span><\/p>\n\u00a0The perimeter of a square is the sum of all the four sides of a square, whereas the Area of a square is defined as the region or the space occupied by a square in the two-dimensional space.<\/span><\/span><\/p>\n3. How is a Square different from a Rectangle?<\/strong><\/span><\/p>\nA square has all its sides are equal in length whereas a rectangle has only its opposite sides are equal in length.<\/p>\n
4. What are the real-life examples of a Square?<\/strong><\/span><\/p>\nSome of the real-life examples of a\u00a0 square are Carrom Board, Square tiles, Square shaped tables, Cubes, Chess Board, etc.<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"An Area is a space or a region occupied by any shape. Square is a two-dimensional figure with four sides, it is also known as a quadrilateral. The area of a square is defined as the number of square units needed to fill a square. In other words, a square is a product of two … Read more<\/a><\/p>\n","protected":false},"author":11,"featured_media":69815,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/Area-of-a-Square-1.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/68619"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=68619"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/68619\/revisions"}],"predecessor-version":[{"id":92288,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/68619\/revisions\/92288"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/69815"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=68619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=68619"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=68619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n
<\/a><\/p>\nArea of a square=side x side<\/p>\n
Perimeter of a Square Formula<\/h4>\n
The perimeter of the square is equal to the sum of all its four sides. The unit of the perimeter remains the same as that of the side-length of a square.<\/p>\n
Perimeter=side+side+side+side=4side unit<\/p>\n
Perimeter =4 x side of the square = 4a unit<\/p>\n
Where ‘a’ is the length of the side of the square.<\/p>\n
Also, Read: Perimeter of a Square<\/a><\/p>\n The length of the diagonals of the square is equal to s\u221a2, where s is the side of the square. The length of the diagonals is equal to each other. By Pythagoras theorem, diagonal is the hypotenuse and the two sides of the triangle formed by the diagonal of the square, are perpendicular and base. Hypotenuse\u00b2=Base\u00b2 + Perpendicular\u00b2<\/p>\n Hence,Diagonal\u00b2=side\u00b2 + side\u00b2<\/p>\n Diagonal=\u221a2side\u00b2, d=s\u221a2<\/p>\n where d is the length of the diagonal of a square and s is the side of the square.<\/p>\n It is a line segment that connects two opposite vertices of the square. Suppose we have four vertices, thus we can have two diagonals within a square. The diagonal of a square is always greater than its sides.<\/p>\n The relation between Diagonal ‘d’ and Side ‘a’ of a square is, d=a\u221a2<\/p>\n The relation between Diagonal ‘d’ and Area ‘A’ of a square is, d=\u221a(2A)<\/p>\n The relation between Diagonal ‘d’ and Perimeter ‘P’ of a square is,d=p\/2\u221a2<\/p>\n Usually, the Area of the Square is measured in the Square Units since each side of the square is the same. Some of the Common Units of Measurement and their equivalent are expressed below.<\/p>\n Have a glance at the Properties of Square and get an idea of them so that you might find them useful while solving related problems. They are as follows<\/p>\n 1. Find the Area of a square of the Side 2.5 cm?<\/strong><\/p>\n Solution: <\/strong><\/p>\n Given, Area of a square of the side is\u00a0 2.5 cm<\/p>\n Area of a square = length x length<\/p>\n Substitute the given value in the above formula,<\/p>\n = 2.5 x\u00a0 2.5 sq. cm<\/p>\n = 6. 25 sq. cm<\/p>\n 2. Find the area of a square of side 49 m?<\/strong><\/p>\n Solution:\u00a0 <\/strong><\/p>\n Given, Area of a square of the side is 49 m<\/p>\n Area of a square\u00a0 = length\u00a0 x\u00a0 length<\/p>\n Substitute the given value in the above formula,<\/p>\n = 49\u00a0 x\u00a0 49 sq. m.<\/p>\n = 2401 sq. m.<\/p>\n 3. Let a square has a side equal to 3 cm. Find out its area, length of diagonal, and perimeter?<\/strong><\/p>\n Solution: <\/strong><\/p>\n Given, side of the square, s= 3 cm<\/p>\n Area of a square= s\u00b2<\/p>\n Therefore, by substituting the value of the side, we get,<\/p>\n 3\u00b2 = 9 cm\u00b2<\/p>\n Length of the diagonal of\u00a0 square = s\u221a2<\/p>\n By substituting the value, we get,<\/p>\n 3 x 1.414 = 4.242<\/p>\n The perimeter of the square = 4 xs<\/p>\n substituting the value in the above formula, we get,<\/p>\n 4 x 3= 12 cm.<\/p>\n 4. Find the area of a square clipboard whose side measures 120 cm?<\/strong><\/p>\n Solution: <\/strong><\/p>\n Given, side of the clipboard\u00a0 = 140 cm = 1.4 m<\/p>\n Area of the clipboard\u00a0 = side x side<\/p>\n substituting the value in the above formula, we get,<\/p>\n Area of the clipboard\u00a0 = 140 cm x 140 cm<\/p>\n = 19,600 sq . cm<\/p>\n = 1.96 sq . m<\/p>\n 5. A wall that is 40 m long and 30 m wide is to be covered by square tiles. The side of each tile is\u00a0 2 m. Find the number of tiles required to cover the wall?<\/strong><\/p>\n Solution:\u00a0 <\/strong><\/p>\n Given, Length of the wall = 40 m<\/p>\n The breadth of the wall = 30 m<\/p>\n Area of the wall = Length x breadth<\/p>\n substituting the length and breadth values, we get<\/p>\n Area of the wall= 40 m x 30 m = 1200 sq. m<\/p>\n side of one tile = 2 m<\/p>\n Area of one tile = side x side<\/p>\n substitute the value in the above formula, we get<\/p>\n Area of one tile =2 m x 2 m= 4 sq. m<\/p>\n No. of tiles required = Area of wall\/ Area of a tile<\/p>\n substitute the value, we get<\/p>\n No.of tiles required = 1200\/ 4 = 300 tiles<\/p>\n \u00a01. What is the Area of a Square Formula?<\/span><\/strong><\/p>\n The area of a square can be calculated by using a formula side x side square units.<\/p>\n 2. Define Perimeter<\/strong> and Area of a Square?<\/strong><\/span><\/p>\n \u00a0The perimeter of a square is the sum of all the four sides of a square, whereas the Area of a square is defined as the region or the space occupied by a square in the two-dimensional space.<\/span><\/span><\/p>\n 3. How is a Square different from a Rectangle?<\/strong><\/span><\/p>\n A square has all its sides are equal in length whereas a rectangle has only its opposite sides are equal in length.<\/p>\n 4. What are the real-life examples of a Square?<\/strong><\/span><\/p>\n Some of the real-life examples of a\u00a0 square are Carrom Board, Square tiles, Square shaped tables, Cubes, Chess Board, etc.<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":" An Area is a space or a region occupied by any shape. Square is a two-dimensional figure with four sides, it is also known as a quadrilateral. The area of a square is defined as the number of square units needed to fill a square. In other words, a square is a product of two … Read more<\/a><\/p>\n","protected":false},"author":11,"featured_media":69815,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/Area-of-a-Square-1.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/68619"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=68619"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/68619\/revisions"}],"predecessor-version":[{"id":92288,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/68619\/revisions\/92288"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/69815"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=68619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=68619"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=68619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Length of Diagonal of a Square<\/h4>\n
Diagonal of Square<\/h4>\n
Area of Square Units<\/h4>\n
\n
Properties of a Square<\/h3>\n
\n
Solved Problems on Area of a Square<\/h3>\n
FAQ’s on Area of a Square<\/h3>\n