Question

In the given figure PQ = 7 cm, QR = 3 cm, then find the area of the shaded
region.
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Answer 1

Answer:

23.56 cm²

Step-by-step explanation:

Find the area of semicircle PSR:

radius = (7 + 3) ÷ 2 = 5 cm

Area of the semicircle = 1/2 πr²

Area of the semicircle = 1/2 π(5)²

Area of the semicircle = 25π/2 cm²

Find the area of semicircle PAQ:

Radius = 7 ÷ 2 = 3.5 cm

Area of the semicircle = 1/2 πr²

Area of the semicircle = 1/2 π(3.5)²

Area of the semicircle = 49π/8 cm²

Find the area of semicircle QTR:

Radius = 3 ÷ 2 = 1.5 cm

Area of the semicircle = 1/2 πr²

Area of the semicircle = 1/2 π(1.5)²

Area of the semicircle = 9π/8 cm²

Find the area of the shaded region:

Area = 25π/2 - 49π/8  +  9π/8

Area = π/4

Area = 23.56 cm²

Answer: 23.56 cm²