A large square is made by arranging a small square surrounded by four congruent rectangles as shown in Fig. 9.53. If the perimeter of each of the rectangle is 16 cm, find the area of the large square.

Solution:

Consider l and b as the length and breadth of the rectangle

Given

Perimeter of one rectangle = 16 cm

We know that

Perimeter of rectangle = 2 (l + b)

By equating it we get

2 (l + b) = 16

Dividing both sides by 2

l + b = 16/2

l + b = 8 cm

As the side of larger square is l + b

Here

Area = side²

Area = (l + b)²

So we get

Area = 8²

Area = 64 cm²

Therefore, the area of the larger square is 64 cm².

✦ Try This: The perimeter of a rhombus is 60 cm and one diagonal is 6 cm long then the length of the other diagonal is

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11

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NCERT Exemplar Class 7 Maths Chapter 9 Problem 101

A large square is made by arranging a small square surrounded by four congruent rectangles as shown in Fig. 9.53. If the perimeter of each of the rectangle is 16 cm, find the area of the large square.

Summary:

A large square is made by arranging a small square surrounded by four congruent rectangles as shown in Fig. 9.53. If the perimeter of each of the rectangle is 16 cm, the area of the large square is 64 cm²

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