Find the area of a parallelogram shaped shaded region of Fig. 9.13. Also, find the area of each triangle. What is the ratio of area of shaded portion to the remaining area of rectangle?
Solution:
It is given that
ABCD is a rectangle
l = 10 cm
b = 6 cm
From the figure
AF = 4 cm
We have to find the area of the shaded portion
We know that
Area of ∆ DAF = 1/2 × base × length
Substituting the values
= 1/2 × 4 × 6
= 12 cm²
Area of rectangle = l × b
Substituting the values
= 10 × 6
= 60 cm²
So we get
Area of shaded region = Area of rectangle - Area of ∆DAF - Area of ∆ BCE
By substituting the values
= (60 - 12 - 12)
= 60 - 24
= 36 cm²
Area of remaining part = Area of Rectangle - Area of shaded portion
Substituting the values
= 60 - 36
= 23 cm²
Ratio = Area of shaded portion : Area of remaining rectangle
Ratio = 36: 24 = 3: 2
Therefore, the ratio of area of shaded portion to the remaining area of rectangle is 3: 2.
✦ Try This: Circumference of a circle is 15 cm. Find its area.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Sample Problem 15
Find the area of a parallelogram shaped shaded region of Fig. 9.13. Also, find the area of each triangle. What is the ratio of area of shaded portion to the remaining area of rectangle?
Summary:
The area of a parallelogram shaped shaded region of Fig. 9.13 is 60 cm², the area of each triangle is 12 cm². The ratio of area of shaded portion to the remaining area of rectangle is 3: 2
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