FIND THE PERIMETER OF EACH PARALLELOGRAM

The formula for the Perimeter of a parallelogram,

Perimeter = 2(a + b)

(where a and b are the sides)

Find the perimeter of each parallelogram.

Problem 1 :

Solution :

Given, side (a) = 7 in and side (b) = 5 in

Perimeter of a parallelogram P = 2 (a + b)

P = 2 (7 + 5)

P = 2 (12)

P = 24 in

So, the perimeter of a parallelogram is 24 in.

Problem 2 :

Solution :

Given, side (a) = 8 yd and side (b) = 9 yd

Perimeter of a parallelogram P = 2 (a + b)

P = 2 (8 + 9)

P = 2 (17)

P = 34 yd

So, the perimeter of a parallelogram is 34 yd.

Problem 3 :

Solution :

Given, side (a) = 10 ft and side (b) = 11 ft

Perimeter of a parallelogram P = 2 (a + b)

P = 2 (10 + 11)

P = 2 (21)

P = 42 ft

So, the perimeter of a parallelogram is 42 ft.

Problem 4 :

Solution :

Given, side (a) = 12 yd and side (b) = 14 yd

Perimeter of a parallelogram P = 2 (a + b)

P = 2 (12 + 14)

P = 2 (26)

P = 52 yd

So, the perimeter of a parallelogram is 52 yd.

Problem 5 :

Solution :

Given, side (a) = 2 ft and side (b) = 4 ft

Perimeter of a parallelogram P = 2 (a + b)

P = 2(2 + 4)

P = 2 (6)

P = 12 ft

So, the perimeter of a parallelogram is 12 ft.

Problem 6 :

Solution:

Given, side (a) = 18 in and side (b) = 6 in

Perimeter of a parallelogram P = 2 (a + b)

P = 2 (18 + 6)

P = 2 (24)

P = 48 in

So, the perimeter of a parallelogram is 48 in.

Problem 7 :

The adjacent sides of a parallelogram measure 13 feet and 1 foot. Determine the perimeter of the parallelogram.

Solution:

Let adjacent side (a) = 13 ft and side (b) = 1 ft

Perimeter of a parallelogram P = 2 (a + b)

P = 2 (13 + 1)

P = 2 (14)

P = 28 ft

So, the perimeter of a parallelogram is 28 ft.

Problem 8 :

What is the perimeter of the parallelogram whose adjacent sides measure 15 yards and 17 yards?

Solution :

Let adjacent side (a) = 15 yd and side (b) = 17 yd

Perimeter of a parallelogram P = 2 (a + b)

P = 2 (15 + 17)

P = 2 (32)

P = 64 yd

So, the perimeter of a parallelogram is 64 yd.

Problem 9 :

The base of the parallelogram is x + 3 cm and height is 4 cm. If the area of the parallelogram is 30 cm². Find the value of x.

Solution :

Area of parallelogram = 30 cm²

base ⋅ height = 30

base = x + 3 and height = 4 cm

4 (x + 3) = 30

x + 3 = 30/4

x + 3 = 7.5

x = 7.5 - 3

x = 4.5 cm

So, the value of x is 4.5 cm.

Problem 10 :

The perimeter of the parallelogram is 30 cm. If the height of the parallelogram is 5 cm and the length of adjacent side is 6 cm, find its base.

Solution :

Perimeter of parallelogram = 30 cm

height = 5 cm

Since it is parallelogram, the opposite sides will be equal.

Sum of sides of all lengths = 30 cm

Let x be the missing base.

2x + 5 + 5 = 30

2x + 10 = 30

2x = 20

x = 20/2

x = 10 cm

So, the missing base is 10 cm.

Problem 11 :

If the base and height of the parallelogram are 360 inches and 8 yards respectively. Find the area of the parallelogram.

Solution :

Base = 360 inches

1 yard = 3 feet

1 feet = 12 inches

8 yards = (8 x 3) feet

= 24 feet

24 feet = 24 x 12

height = 288 inches

Area of parallelogram = Base x height

= 360 x 288

= 103680 square inches

Problem 12 :

What is the area of parallelogram with base 2.85 mm, height 12.87 mm ?

Solution :

Base = 2.85 mm

height = 12.87 mm

Area of parallelogram = 2.85 x 12.87

= 36.679

Approximately 36.68 mm²

Problem 13 :

The area of parallelogram is 62 cm² and its height is 7 cm, what is its base?

Solution :

Area of parallelogram = 62 cm²

Base = b

height = 7 cm

b x 7 = 62

b = 62/7

b = 8.85

So, the base of the parallelogram is 8.85 cm.

Problem 14 :

The area of rectangle is 87 cm² and its height is 9.2 cm, what is its base?

Solution :

Area of parallelogram = 87 cm²

Base = b

height = 9.2 cm

b x 9.2 = 87

b = 87/9.2

b = 9.45

So, the base of the parallelogram is 9.45 cm.