WORD PROBLEMS INVOLVING PERIMETER OF THE 2D SHAPES

Problem 1 :

If the perimeter of a square is 16, what is its area?

Solution :

Perimeter of square = 16

Perimeter of square = 4 × a

So, the required area is 16 square units.

Problem 2 :

If a triangle has area of 35 and length of 16, what is its base?

Solution :

Area = 35

Length = 16

Area of triangle = 1/2 × b × h

35 = 1/2 × b × 16

35 = 8 × b

b = 35/8

b = 4.37

So, base of the triangle is 4.37.

Problem 3 :

If a triangle has area of 32 and height of 5, what is its base?

Solution :

Area = 32

Height = 5

Area of triangle = 1/2 × b × h

32 = 1/2 × b × 5

32 = 2.5 × b

b = 32/2.5

b = 12.8

So, base of the triangle is 12.8.

Problem 4 :

If the perimeter of a rectangle is 14 and the length is 5 more than the width, what is its area?

Solution :

Perimeter of rectangle = 14

Width = x, Length = x + 5

Perimeter of rectangle = 2(l + b)

14 = 2(x + 5 + x)

14 = 2(2x + 5)

2x + 5 = 7

2x = 2

x = 1

Area of rectangle = length × width

= 6 × 1

= 6

So, the area of rectangle is 6.

Problem 5 :

If perimeter of a rectangle is 14 and the length is 4 more than the width, what is its area?

Solution :

Given, Perimeter of rectangle = 14

Width = x

Length = x + 4

Perimeter of rectangle = 2(l + b)

14 = 2(x + 4 + x)

14 = 2(2x + 4)

2x + 4 = 7

x = 3/2

Area of rectangle = length × width

= 5.5 × 1.5

= 8.25

So, the area of rectangle is 8.25.

Problem 6 :

If a square has a side of 1/2 inch, what is its area?

Solution :

Given, side a = 1/2 inch

Area of square = a²

= (1/2)²

= 1/4 in²

So, area of the square is 1/4 in².

Problem 7 :

If a rectangle has dimensions of 3/4 inch and 5/8 inch, what is its area?

Solution :

length = 3/4 inch

Width = 5/8 inch

Area of rectangle = length × width

= 3/4 × 5/8

= 15/32 in²

So, the area of rectangle is 15/32 in².

Problem 8 :

If a rectangle has area of 32 2/3 inch and a length of 14 inch, what is its width?

Solution :

Area of rectangle = 32 2/3 inch

Length = 14 inch

Area of rectangle = length × width

32 2/3 = 14 × width

98/3 = 14 × width

Width = 7/3 inch

So, the width of rectangle is 7/3 inch.

Problem 9 :

If a rectangle has area of 38 inch and a length of 4 ¾ inch, what is its width?

Solution :

Area of rectangle = 38 inch

Length = 4 ¾ inch

Area of rectangle = length × width

38 = 19/4 × width

Width = 38 / (19/4)

Width = 8 inch

So, the width of rectangle is 8 inch.

Problem 10 :

A nursery school playground is 160 m long and 80 m wide. In it 80 m x 80 m is kept for swings and in the remaining portion, there are 1.5 m wide path parallel to its width and parallel to its remaining length shown. The remaining area is covered by grass. Find the area covered by grass.

Solution :

Area of play ground = 160 x 80

= 12800 square meter

Area of path = 80 x 1.5

= 120 square meter

Area of swing = 80 x 80

= 6400

Area of path horizontally = (80-1.5) x 1.5

= 78.5 x 1.5

= 117.75 square meter

Area covered by grass = 12800 - (6400 + 120 + 117.75)

= 12800 - 6637.75

= 6162.25 square meter

Problem 11 :

Find the area of a parallelogram shaped region. Also find the area of each triangle. What is the ratio of the shaded portion to the remaining area of rectangle ?

Solution :

Base of the parallelogram = 10 - 4 ==> 6 cm

Height = 6 cm

Area of parallelogram = base x height

= 6 x 6

= 36 square cm

Area of triangles = 2 x 1/2 x base x height

= 6 x 4

= 24 square cm

Area of rectangle = length x width

= 10 x 6

= 60 square cm

Ratio between shaded portion : area of remaining part

= 36 : 24

= 3 : 2