Question

OA and OB are mutually perpendicular radii of a circle find the area of minor segment if the perimeter of corresponding minor sector is 20 cm

Answer 1

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Answer 2

OA and OB are mutually perpendicular radii

⇒ OA and OB forms a right angle,

⇒ ΔOAB is a quarter of the circle

Find r:

Perimeter of the sector = 1/4 (2πr) + 2r

Given Perimeter of the sector = 20 cm

1/4 (2πr) + 2r = 20 cm

2πr + 8r = 80

r ( 2π + 8) = 80

r = 5.6 cm

Find the area of the sector:

Area of the sector = 1/4 (πr²)

Area of the sector = 1/4 π(5.6)² = 24. 64 cm²

Find the area of the triangle:

Area of the triangle = 1/2 x base x height

Area of the triangle = 1/2 x 5.6 x 5.6 = 15.68 cm²

Find the area of the minor segment:

Area of the segment = Area of the sector - Area of the triangle

Area of the segment = 24. 64 - 15.68 = 8.96 cm²

Answer: Area of the segment = 8.96 cm²