In the given figure, FD E is a quadrant. ABCD is a rectangle with BC = 6 cm. CE = 2cm,
calculate the area of the shaded region. (π = 3.14)
a) 20.5cm square
b) 30.5 cm square
ç) 21.5 cm square
d) 30 cm square
Answers
Given:
In the given figure, FD E is a quadrant. ABCD is a rectangle with BC = 6 cm. CE = 2cm,
To find:
Calculate the area of the shaded region.
Solution:
Consider the attached figure while going through the following steps.
Let 'x' be the value of the length 'CD'.
As the radii of the quadrant are same, thus,
DE = BD
√ [6² + x²] = x + 2
square on both the sides.
6² + x² = (x + 2)²
6² + x² = x² + 4 + 4x
36 = 4 + 4x
32 = 4x
x = 8 cm
Therefore, the radius of the quadrant FDE is, 8 + 2 = 10 cm
The area of the quadrant FDE is,
A₁ = 1/4πr²
A₁ = 1/4 × 3.14 × 10²
A₁ = 78.5 cm²
The area of the rectangle ABCD is,
A₂ = l × b
A₂ = 6 × 8
A₂ = 48 cm²
Therefore, the area of the shaded portion is,
A = A₁ - A₂
A = 78.5 - 48
A = 30.5 cm²
Therefore, the area of the shaded portion is, 30.5 cm²
