Question

Find the area of the shaded portion in the following figure.

Answer 1

Given: Parallel sides of trapezium are $160cm$ and $120cm$, height is $100cm$

Radius of circle $=7cm$

Lenght of rectangle $=40cm$ and Breadth of rectangle $=20cm$

Area of trapezium $=\frac{1}{2}\times \text{[Sum of parallel sides]}\times \text{Height}$

$=\frac{1}{2}\times (120+160)\times 100$

$=\frac{1}{2}\times 280\times 100$

$=\frac{28000}{2}=14000c{m}^2$

Area of rectangle $=Length\times Breadth=40\times 20=800c{m}^2$

Area of circle $=\pi r^2=\frac{22}{7}\times 7\times 7$

$=154c{m}^2$

Area of shaded portion $=$Area of trapezium $-$ Area of rectangle $-$ Area of circle

$\therefore$ Area of shaded portion$=14000-800-154$

$=13046c{m}^2$