3 Tutor System
Starting just at 265/hour

# Find the area of the shaded region in figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Area of the square ABCD $$= \ (14)^2 \ = \ 196$$ cm2

Diameter of the semicircles = AD or BC = 14 cm

$$\therefore$$ Radius of each semicircle $$= \ 7$$ cm

Area of the semicircular regions $$= \ 2 \ × \ \frac{1}{2} \pi \ r^2 \ = \ \pi r^2$$

$$= \ \frac{22}{7} \ × \ 49 \ = \ 154$$cm2
$$\therefore$$ Area of the shaded portion

= Area of the square ABCD - Area of the semicircular regions

$$= \ 196 \ - \ 154 \ = \ 42$$cm2