Question

A restaurant POQR is being constructed in the middle of a circular lake. The circle, which has its center at O is touching the mid-points of the boundary ABCD as shown in the figure. AB=CD and AD=BC. If BC=8 cm, then the area of AQOP is

• A. $\frac{1}{4}\times$ Area of ABCD
• B. $\frac{1}{2}\times$ Area of ABCD
• C. $\frac{1}{8}\times$ Area of ABCD
• D. None of these

Answer 1

The correct option is A

$\frac{1}{4}\times$ Area of ABCD

Given, BC = 8 cm
$\Rightarrow AB=8cm[\because AB=BC]$
Now, $AP=\frac{1}{2}AB=4cm$
$\therefore$ Area of AQOP $=4\times 4=16c{m}^2$
and area of $ABCD=8\times 8=64c{m}^2$
$\Rightarrow \frac{AreaofAQOP}{AreaofABCD}=\frac{16}{64}=\frac{1}{4}$
$\Rightarrow AreaofAQOP=\frac{1}{4}\times AreaofABCD$