Question

In the figure, ABCD is a square with side 10. BFD is an 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. $100-257\pi$
• C. $50\pi -100$
• D. $25\pi -100$

Answer 1

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

Area of the portion FBCD $=\frac{1}{4}\times \pi \times (10{)}^2=25\pi$

Area of the $\Delta BCD=\frac{1}{2}\times 10\times 10=50$
Area of the portion DFBOD = 2 x Area of region DFBO = 2 x ($25\pi$ - 50) = $50\pi -100$