Question

Given below is a combination figure of square ABCD of side 26cm and four circles. Find the area of the shaded region.

• A. 530.64 $c{m}^2$
• B. 402.83$c{m}^2$
• C. 360$c{m}^2$
• D. 480.53$c{m}^2$

Answer 1

The correct option is A

530.64 $c{m}^2$

The given figure forms four sectors:

Area of a sector of angle $\theta =\frac{\theta }{{360}^{\circ }}\times \pi r^2$

Area of one sector APS = $\frac{{90}^{\circ }}{{360}^{\circ }}\times \pi \times {13}^2$= 132.66 $c{m}^2$

Total area of shaded region = Area of four sectors
= 4 × 132.66 $c{m}^2$
= 530.64$c{m}^2$