Question

ABCD is a flower bed. If OA = 21m and OC = 14m. Find the area of the bed in $m^2$.

• A. 180.30
• B. 921
• C. 190
• D. 192.50

Answer 1

The correct option is D

192.50

Area of a sector with angle $\theta$ is given by =$\frac{\theta }{360°}$ $\times$ $\pi$ $\times$ $r^2$ ( where $\theta$ is the angle made by the sector )
Required area = Area of sector OABO – Area of sector OCDO

The angle formed by the sector OABO and sector OCDO = 90°
$=\frac{90}{360}\times \frac{22}{7}\times (21{)}^2–\frac{90}{360}\times \frac{22}{7}\times (14{)}^2$
$=\frac{1}{4}\times \frac{22}{7}\times \left\{\right(21{)}^2–\left(14{)}^2\right\}$
$=\frac{1}{4}\times \frac{22}{7}\times \left\{\right(35\left)\right(7\left)\right\}$ $[a^2-b^2=(a+b\left)\right(a-b\left)\right]$
=192.50 $m^2$