Question

In the given figure, $ABCD$ is a square with side $10cm$. $BFD$ is an arc of a circle with center $C$ and $BGD$ is an arc of a circle with center $A$. What is the area of the shaded region in square centimeters?

• A. $100-50\pi$
• B. $100-25\pi$
• C. $50\pi -100$
• D. $25\pi -100$

Answer 1

The correct option is C $50\pi -100$

Area of the portion DGBC $=$ Area of the quadrant of a circle with center C and radius 10 cm

$=\frac{1}{4}\times \pi \times (10{)}^2=25\pi c{m}^2$

Area of $\Delta BCD=\frac{1}{2}\times 10\times 10c{m}^2=50c{m}^2$

$\therefore$ Area of portion BEDOB $=$ Area of quad $2\times (25\pi -50)c{m}^2-$ Area of $\Delta BCD$

$=(25\pi -50)c{m}^2$

Area of shaded portion $=(50\pi -100)c{m}^2$