Find the area of the shaded region in Fig. 12.19, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.

Question

Philoid · Accepted Answer

Here, OR is the hypotenuse of as lines from two ends of diameter always make a right angle when they meet at the circumference of that circle.

Hence,

OR² = PQ² + PR²

OR² = 24² + 7²

OR² = 576 + 49

OR = 25 cm

Or, radius = 12.5cm

Area of triangle = 1/2 * base *height

= 1/2 * 24 *7

Area of semicircle = ²

= ²

= 245.3125 sq cm

Hence,

Area of shaded region = 245.3125 – 84

= 161.3125 sq cm