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.
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.
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?
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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