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

The Correct Option is C

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): \(50\pi-100\)