Question

PQ=24cm, PR=7cm and O is the center of the circle find the area of the shaded region(Π=3.14)

Answer 1

Answer:

161.54

Step-by-step explanation:

PQ = 24 cm and PR = 7 cm

∠P = 90° (Angle in the semi-circle)

∴ QR is hypotenuse of the circle = Diameter of the circle.

By Pythagoras theorem,

QR2 = PR2 + PQ2

⇒ QR2 = 72 + 242

⇒ QR2 = 49 + 576

⇒ QR2 = 625

⇒ QR = 25 cm

∴ Radius of the circle = 25/2 cm

Area of the semicircle = (π R2)/2

= (22/7 × 25/2 × 25/2)/2 cm2

= 13750/56 cm2 = 245.54 cm2

Area of the ΔPQR = 1/2 × PR × PQ

= 1/2 × 7 × 24 cm2

= 84 cm2

Area of the shaded region = 245.54 cm2 - 84 cm2 = 161.54 cm2