The following diagram shows part of a fan. OAD and OFG are sectors of a circle with centre O, having radius 24 cm. The central angle of the sectors is 45° as shown in the figure. B, C, H and E lie on a circle with centre O and radius 8 cm. What is the shaded area (in cm²)?
Take π = 3.14

Solution (By Examveda Team)

It is clear from the figure
Area of shaded region = Area of sector of OFG and OAD + Area of circle BCHE - area of sector OHE and OBC
$$\eqalign{ & = 2 \times \frac{\theta }{{360}} \times \pi {r^2} + \pi {r^2} - 2 \times \frac{\theta }{{360}} \times \pi {r^2} \cr & = 2 \times \frac{{45}}{{360}} \times 3.14 \times 24 \times 24 + 3.14 \times {8^2} - 2 \times \frac{{45}}{{360}} \times 3.14 \times {8^2} \cr & = \frac{1}{4} \times 3.14 \times 24 \times 24 + 3.14 \times 64 - \frac{1}{4} \times 3.14 \times 64 \cr & = 3.14 \times \left( {144 + 64 - 16} \right) \cr & = 3.14 \times 192 \cr & = 602.88{\text{ Answer}} \cr} $$