{"id":34768,"date":"2023-10-15T10:18:38","date_gmt":"2023-10-15T04:48:38","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=34768"},"modified":"2023-11-10T11:37:06","modified_gmt":"2023-11-10T06:07:06","slug":"area-of-the-path","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/area-of-the-path\/","title":{"rendered":"Area of the Path | How to find the Area of the Path?"},"content":{"rendered":"

Path is nothing but the measure of boundaries of the shapes. The area of the path is defined as the region occupied by the shape inside or outside. Here we can apply the concept of Area of rectangle or area square to find the area of paths. This is the major concept in the basic theory of Mensuration<\/strong><\/a>. The students can learn the different techniques to find the area of the path of different shapes like rectangle, square, circle, etc.<\/p>\n

What is the Area of Path?<\/h2>\n

The area of the path is the subtraction of the area of the outer rectangle\/square and the area of the inner rectangle\/square. It is defined as the space left between the area of two 2-d figures or paths. This article helps to learn the theory of the area of the path in depth.<\/p>\n

Area of the Path Formula<\/h3>\n

Area of the path = area of outer rectangle – area of inner rectangle
\nArea of the path = area of outer square – area of inner square<\/p>\n

Solved Problems on Area of the Path<\/h3>\n

Here we use the concept of the area of rectangle and area of the square. Know how to calculate the area of the path with the help of the solved example problems.<\/p>\n

1. A rectangular plot is 20 cm long and 15 cm wide. The inner rectangular plot is 12 cm long and 10 cm wide. Draw the diagram of the rectangular plot and find the area of the path?<\/strong><\/p>\n

Solution:
\n\"Area
\nGiven the length of the outer rectangle is 20 cm
\nWidth of the outer rectangle is 15 cm
\nWe know that,
\nArea of the rectangle = l \u00d7 w
\nA = 20 cm \u00d7 15 cm
\nA = 300 sq. cm
\nAlso given the length of the inner rectangle = 12 cm
\nWidth of the inner rectangular plot = 10 cm
\nWe know that,
\nArea of the rectangle = l \u00d7 w
\nA = 12 cm \u00d7 10 cm
\nA = 120 sq. cm
\nTotal Area of the path = 300 sq. cm – 120 sq. cm = 180 sq. cm<\/p>\n

2. A park is of length 30 m and 20 m wide. A path 1.5 m wide is constructed outside the rectangular garden. Find the area of the path?<\/strong><\/p>\n

Solution:<\/p>\n

\"Area<\/p>\n

Given the length of the inner rectangle = 30 meter
\nThe wodth of the inner rectangle = 20 meter
\nWe know that,
\nArea of the rectangle = l \u00d7 w
\nA = 30 m \u00d7 20 m
\nA = 600 sq. meter
\nAB = 20 + 1.5 + 1.5 = 23 m
\nBC = 30 + 1.5 + 1.5 = 33 m
\nArea of the outer rectangle = l \u00d7 w
\nA = 33 m \u00d7 23 m
\nA = 759 sq. meter
\nArea of the path = Area of outer rectangle – Area of inner rectangle
\nTherefore Area of the path = 759 sq. m – 600 sq. m
\nA = 159 square meters
\nThus the area of the path of rectangular garden is 159 sq. meters.<\/p>\n

3. A path 10 m wide runs along inside the square park of side 1000 m. Find the area of the path?\u00a0<\/strong><\/p>\n

Solution:
\n\"Area
\nGiven that,
\nA path 10 m wide runs along inside the square park of side 1000 m.
\nPS = PQ = QR = RS = 1000m
\nFind the sides of the inner square.
\nWidth = 10m
\nAB = 1000 – 10 – 10 = 980m
\nAB = BC = CD = AD = 980 m
\nWe know that
\nArea of the square = side \u00d7 side
\nA = 1000 \u00d7 1000 = 1,000,000 m\u00b2
\nArea of the inner square = s \u00d7 s
\nA = 980 \u00d7 980 = 960,400 m\u00b2
\nArea of the path = 1,000,000 m\u00b2 – 960,400 m\u00b2
\n= 39,600m\u00b2
\nThus the area of the path is 39,600m\u00b2<\/p>\n

4. A rectangular box is 10 cm long and 8 cm wide. A path of the uniform width is 5 cm. Find the area of path?<\/strong><\/p>\n

\"Area<\/p>\n

Solution:
\nGiven,
\nA rectangular box is 10 cm long and 8 cm wide. A path of the uniform width is 5 cm
\nFind the length and width of the outer rectangle
\nAD = 10cm + 5cm + 5cm = 20cm
\nAB = 8cm + 5cm + 5cm = 18cm
\nArea of the outer rectangle = l \u00d7 w
\nA = 20cm \u00d7 18cm
\nA = 360 sq. cm
\nArea of the inner rectangle = l \u00d7 w
\nA = 10cm \u00d7 8cm
\nA = 80 sq. cm
\nArea of the path = Area of outer rectangle – Area of inner rectangle
\nA = 360 sq. cm – 80 sq. cm
\nA = 280 sq. cm
\nThus the area of path is 280 sq. cm<\/p>\n

5. A 1m wide path runs outside and around a rectangular park of length 6m and width 4m. Find the area of the path?<\/strong><\/p>\n

\"Area<\/p>\n

Solution:
\nGiven,
\nA 1m wide path runs outside and around a rectangular park of length 6m and width 4m.
\nArea of inner rectangle = l \u00d7 w
\nA = 6m \u00d7 4m
\nA = 24 sq. m
\nArea of outer rectangle = (6m + 1m + 1m) \u00d7 (4m + 1m + 1m)
\nA = 8m \u00d7 6m
\nA = 48 sq. m
\nArea of the path = Area of the outer rectangle – Area of inner rectangle
\nA = 48 sq. m – 24 sq. m
\nA = 24 sq. meters
\nThus the area of the path is 24 sq. meters.<\/p>\n

FAQs on Area of the Path<\/h3>\n

1. How to find the area of the path?<\/strong><\/p>\n

We can find the area of a path by subtracting the area of outer shapes and the area of inner shapes.<\/p>\n

2. What is the formula for Area of Path?<\/strong><\/p>\n

Area of the path = Area of outer rectangle\/square – Area of inner rectangle\/square<\/p>\n

3. How to calculate the area of the path for square?<\/strong><\/p>\n

You can calculate the Area of the path using the formula Area of Path = Area of outer square – Area of inner square<\/p>\n","protected":false},"excerpt":{"rendered":"

Path is nothing but the measure of boundaries of the shapes. The area of the path is defined as the region occupied by the shape inside or outside. Here we can apply the concept of Area of rectangle or area square to find the area of paths. This is the major concept in the basic … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34768"}],"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\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=34768"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34768\/revisions"}],"predecessor-version":[{"id":92711,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/34768\/revisions\/92711"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=34768"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=34768"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=34768"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}