Question

Given figure shows a flower bed ABCD. If OA = 20 m and OC = 15 m. Find the area of the shaded portion.

• A. 145.4 $m^2$
• B. 160.2 $m^2$
• C. 137.5 $m^2$
• D. 157.5 $m^2$

Answer 1

The correct option is C 137.5 $m^2$

Given: The angle formed by the sectors OABO and OCDO = 90° and
Radius of sectors OABO and OCDO are 20 m and 15 m respectively.

Area of a sector subtending angle $\theta$ is given by =$\frac{\theta }{360°}$ $\times$ $\pi$ $\times$ $r^2$

Required area = [Area of sector OABO – Area of sector OCDO]

$=\frac{90}{360}\times \frac{22}{7}\times (20{)}^2–\frac{90}{360}\times \frac{22}{7}\times (15{)}^2$
$=\frac{1}{4}\times \frac{22}{7}\times \left\{\right(20{)}^2–\left(15{)}^2\right\}$
$=\frac{1}{4}\times \frac{22}{7}\times \left\{\right(20+15\left)\right(20-15\left)\right\}[\because a^2-b^2=(a+b\left)\right(a-b\left)\right]$
$=\frac{1}{4}\times \frac{22}{7}\times \left\{\right(35\left)\right(5\left)\right\}$
= 137.5 $m^2$

$\therefore$ Area of shaded portion = 137.5 $m^2$