Question

find the area of the shaded region in the above figure where PQRS is a rectangle 30 cm long and the two circles have the same radii (π = 3.14)​

Answer 1

from the figure,

radius of the circle = (1/4)(length of rectangle PQRS) cm

r = (1/4)(30) cm

r = 15/2 cm

diameter of the circle = breadth of rectangle

hence, diameter = 2r = 2x(15/2) = 15 cm

For the circles;

r = 15/2 cm

π = 3.14

For the rectangle;

l = 30 cm

b = 15 cm

now, area of shaded region

= ar(rectangle) - 2xar(circle)

$= (l \times b) - 2(\pi \: {r}^{2} ) \\ = (30 \times 15) - 2( \frac{22}{7} \times \frac{15}{2} \times \frac{15}{2} ) \\ = 450 - (2 \times \frac{ 22}{7} \times \frac{15}{2} \times \frac{15}{2} ) \\ = 450 - ( \frac{11 \times 15 \times15}{7} ) \\ = 450 - ( \frac{2475}{7} ) = 450 - 353.57143 \\ = 96.428571 \\ = 96.43 \: {cm}^{2}$

Hence, area of the shaded region is 96.43 cm²