Let’s get started with some fun questions based on the area of a parallelogram! These questions follow the latest exam pattern and are great for students in Class 7 and 8. All questions are designed as per the CBSE syllabus (2022–2023) and the NCERT curriculum.

Before solving the problems, let’s quickly recall the concept. The area of a parallelogram is the amount of flat space it covers. A parallelogram is a four-sided shape where opposite sides are equal in length and parallel to each other.

To find how much space it takes up, we use a simple formula:

Area = Base × Height

Here, the base is the length of the bottom side, and the height is the vertical distance from the base to the top side. The answer is always in square units.

Here are some questions on the area of a parallelogram along with their solutions:

Example 1: If the base of a parallelogram is 5 cm and the height is 8 cm, what is its area?

Solution: Given,

Base of the parallelogram = 5 cm

Height of the parallelogram = 8 cm

Area of the parallelogram = Base x Height = 5cm x 8cm = 40 cm 2

Example 2: Calculate the area of a parallelogram with a base of 14 centimeters and a height of 6 centimeters.

Solution:

Area of parallelogram = Base * Height

Area = (14 cm) · (6 cm)

A = 84 cm 2

Example 3: The base of a parallelogram is 3 centimeters and its area is 24 square centimeters. Can you find the height?

Solution:

Area = Base x Height

24 cm 2 = 3 cm x Height

24 cm 2 ÷ (3 cm) = Height

Height = 8 cm

Example 4: If the base of a parallelogram is x + 2 cm and the height is 5 cm, and the area of the parallelogram is 25 cm 2 , can you find the value of x?

Solution: Given,

Base = x + 2 cm

Height = 5 cm

Area of parallelogram = 25 cm 2

Base x height = 25 cm 2

(x+2) (5) = 25 cm 2

5x + 10 = 25

5x = 25 – 10

5x = 15

x = 15/5 = 3

Therefore, the value of x is 3 cm.

Example 5: If the perimeter of a parallelogram is 36 cm, the height is 6 cm and the length of the adjacent side is 7 cm, can you find its area?

Solution: Given,

Perimeter of parallelogram = 36 cm

Height = 6cm

Length of adjacent sides = 7 cm

Perimeter of parallelogram = 2 (Adjacent side + Base) = 2 (7 + B)

36 = 2 (7 + B)

7 + B = 18

B = 18 – 7 = 11 cm

Now,

Area of parallelogram = Base x height

= 11 x 6

= 66 cm 2

Example 6: Can you find the area of a parallelogram whose base = 6.4 cm and height = 7.1 cm?

Solution: Given,

Base = 6.4 cm

Height = 7.1 cm

Area of parallelogram = base x height

= 6.4 x 7.1

= 45.44 cm 2

Example 7: Can you find the area of the parallelogram given in the below figure?

Solution: From the given figure, the parallelogram has:

Base = 10 in

Height = 8 in

Area of parallelogram = base x height

= 10 x 8 in 2

= 80 in 2

Example 8: Can you find the area of the parallelogram given in the figure?

Solution: Given,

Base = 10.6 ft

Height = 4.9 ft

Area of parallelogram = Base x Height

= 10.6 x 4.9

= 51.94 ft 2

Example 9: Can you calculate the area of the parallelogram given in the figure?

Solution: Given, the base and height of the parallelogram are:

Base = 10/5 yd

Height = 15/5 yd

Area of parallelogram = Base x Height

= 10/5 x 15/5

= 30/5 yd 2

Example 10: If the base and height of a parallelogram are 400 in and 9 yd respectively, can you find the area of the parallelogram?

Solution: Given,

Base = 400 in = 400/36 = 11.11 yd

Height = 9 yd

Area of parallelogram = Base x Height

= 11.11 x 9

= 100 yd 2

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