Question

In the given figure, $PQRS$ is a rectangle of $8cm\times 6cm$ inscribed in a circle. What is the area of the shaded portion?

• A. $30.57c{m}^2$
• B. $37.52c{m}^2$
• C. $40.56c{m}^2$
• D. $28.56c{m}^2$

Answer 1

The correct option is A $30.57c{m}^2$

Diameter of the circle $=$ Diagonal of the rectangle
$\Rightarrow S{Q}^2=S{R}^2+Q{R}^2=8^2+6^2=64+36=100$

$\Rightarrow SQ=\sqrt{100}cm=10cm$
$\therefore$ Area of shaded portion $=$ Area of circle $-$ Area of rectangle $PQRS$.
$=\frac{22}{7}\times 5\times 5-8\times 6$
$=78.57-48=30.57c{m}^2$