Area of Parallelogram Questions

Area of parallelogram questions and answers are provided here. The questions are prepared as per the latest exam pattern for Class 7 and 8 students. The problems of the area of a parallelogram are based on the CBSE syllabus (2022-2023) and the NCERT curriculum.

Definition: The area of the parallelogram is the region bounded by it in a two-dimensional plane. A parallelogram is a four-sided polygon, and the space covered within its four sides is its area. The opposite sides of a parallelogram are parallel to each other and equal in measure. The formula to find the area of a parallelogram is given by:

Area = Base x Height (Square units)

Area of Parallelogram Questions and Solutions

Q.1: What is the area of a parallelogram with base equal to 4 cm and height equal to 7 cm?

Solution: Given,

Base length of parallelogram = 4 cm

Height of parallelogram = 7 cm

Area of parallelogram = base x height = 4cm x 7cm = 28 cm2

Q.2: Find the area of this parallelogram with a base of 12 centimeters and a height of 5 centimeters.

Solution:

Area of parallelogram = Base * Height

Area = (12 cm) · (5 cm)

A = 60 cm2

Q.3: The area of a parallelogram is 32 square centimeters and the base is 4 centimeters. Find the height.

Solution:

Area = Base x Height

32 cm2 = 4 cm x Height

32 cm2 ÷ (4 cm) = Height

Height = 8 cm

Q.4: The base of a parallelogram is x + 3 cm and the height is 4 cm. If the area of the parallelogram is 30 cm2, find the value of x.

Solution: Given,

Base = x + 3 cm

Height = 4 cm

Area of parallelogram = 30 cm2

Base x height = 30 cm2

(x+3) (4) = 30 cm2

4x + 12 = 30

4x = 30 – 12

4x = 18

x = 18/4 = 4.5

Therefore, the value of x is 4.5 cm.

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

Solution: Given,

Perimeter of parallelogram = 30 cm

Height = 5cm

Length of adjacent sides = 6 cm

Perimeter of parallelogram = 2 (Adjacent side + Base) = 2 (6 + B)

30 = 2 (6 + B)

6 + B = 15

B = 15 – 6 = 9 cm

Now,

Area of parallelogram = Base x height

= 9 x 5

= 45 cm2

Q.6: What is the area of parallelogram whose base = 5.4 cm and height = 6.1 cm?

Solution: Given,

Base = 5.4 cm

Height = 6.1 cm

Area of parallelogram = base x height

= 5.4 x 6.1

= 32.94 cm2

Q.7: Find the area of parallelogram given in the below figure.

Area of Parallelogram Questions 1

Solution: From the given figure, the parallelogram has:

Base = 9 in

Height = 7 in

Area of parallelogram = base x height

= 9 x 7 in2

= 63 in2

Q.8: Find the area of parallelogram given in the figure.

Area of Parallelogram Questions 2

Solution: Given,

Base = 9.6 ft

Height = 3.9 ft

Area of parallelogram = Base x Height

= 9.6 x 3.9

= 37.44 ft2

Q.9: What is the area of parallelogram given in the figure?

Area of Parallelogram Questions 3

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

Base = 9/4 yd

Height = 12/5 yd

Area of parallelogram = Base x Height

= 9/4 x 12/5

= 27/5 yd2

Q.10: If base and height of parallelogram are 360 in and 8 yd respectively, find the area of parallelogram.

Solution: Given,

Base = 360 in = 360/36 = 10 yd

Height = 8 yd

Area of parallelogram = Base x Height

= 10 x 8

= 80 yd2

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