PROBLEMS ON AREA AND PERIMETER OF SQUARE AND RECTANGLE

Find area and perimeter of the square and rectangle given below. 

Problem 1 :

Solution :

Area  :

length = 5 cm

width = 3 cm

Area of a rectangle = l × w

= 5 × 3

= 15 cm²

Perimeter :

Perimeter of a rectangle = 2(l + w)

= 2(5 + 3)

= 2(8)

= 16 cm

Problem 2 :

Solution :

Area  :

side = 7 cm

Area of a square = a²

= (7)²

= 49 cm²

Perimeter :

Perimeter of a square = 4 × a

= 4 × 7

= 28 cm

Problem 3 :

Solution :

Area  :

length = 6 cm

width = 20 cm

Area of a rectangle = l × w

= 6 × 20

= 120 cm²

Perimeter :

Perimeter of a rectangle = 2(l + w)

= 2(6 + 20)

= 2(26)

= 52 cm

Problem 4 :

Solution :

Area  :

length = 17 cm

width = 7 cm

area of a rectangle = l × w

= 17 × 7

= 119 cm²

Perimeter :

Perimeter of a rectangle = 2(l + w)

= 2(17 + 7)

= 2(24)

= 48 cm

Problem 5 :

Solution :

Area  :

length = 36 mm

width = 19 mm

area of a rectangle = l × w

= 36 × 19

= 684 mm²

Perimeter :

Perimeter of a rectangle = 2(l + w)

= 2(36 + 19)

= 2(55)

= 110 mm

Problem 6 :

For the rectangle given below, find the width and perimeter of the rectangle.

Solution :

Given, area of of rectangle = 2.7 m²

Length = 1.8 m,  width = x

1.8 (x) = 2.7

x = 2.7/1.8

x = 1.5

Perimeter of the rectangle = 2(l + w)

= 2(1.8 + 1.5)

= 2(3.3)

= 6.6 m

Problem 7 : 

For the rectangle given below, find the length of the rectangle.

Solution :

Given, area of square = 7875 m²

side a = 75 m

Perimeter of a square = 4 × a

= 4 × 75

= 300 m

Problem 8 :

For the rectangle given below, find the width of the rectangle.

Solution :

Area :

length = 9 cm

Area of a rectangle = l × w

54 = 9 × w

54/9 = w 

6 = w

w = 6 cm

Perimeter :

Perimeter of a rectangle = 2(l + w)

= 2(9 + 6)

= 2(15)

= 30 cm

The perimeter of each shape is given. Find the length of the missing side.

Problem 9 :

Solution :

Length = 8 cm

Perimeter = 26 cm

let x be the missing side.

Perimeter of a rectangle = 2(l + w)

26 = 2(8 + x)

26 = 16 + 2x

2x = 26 - 16

2x = 10

x = 10/2

x = 5 cm

So, width of the rectangle is 5 cm.

Problem 10 :

Solution :

Width = 14 cm

Perimeter = 80 cm

let x be the length of the rectangle.

Perimeter of a rectangle = 2(l + w)

80 = 2(x + 14)

80 = 2x + 28

2x = 80 - 28

2x = 52

x = 52/2

x = 26 cm

So the length of the rectangle is 26 cm.

Problem 11 :

Solution :

Perimeter = 20 cm

Let x be the missing side.

Perimeter of a square = 4 × a

20 = 4 × x

20/4 = x

x = 5 cm

So, side length of the square is 5 cm.