Question

In the figure, ABCD is a square with side 10. BFD is dn arc of a circle with centre C. BGD is an arc of a circle with centre A. What is the area of the shaded region?

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

Answer 1

Answer: (C)

$50\pi-100$

Answer 2

Side of square = Radius of arc = 10 cm
Now, area of shaded region =$2\times[ area (sector ABD) -area ( \Delta ABD)]$
⇒$2\times[ (\frac{\theta}{360^\circ}\times \pi r^2)-\frac{1}{2}\times b \times h]$
⇒$2\times[ (\frac{90^\circ}{360^\circ}\times \pi \times 100)-\frac{1}{2}\times 10 \times 10]$
⇒ $2\times(25\pi-50)$
⇒$(50\pi-100)\space cm^2$

The correct option is (C): $50\pi-100$