Question

Pq and rs are the two perpendicular diameter of the circle with centre o if op =28 cm find the area of the shaded region
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Answer 1

Given: 

Radius of larger circle,(OA) R = 7 cm

Diameter of smaller circle,(OD) = 7 cm

Radius of smaller  circle = 7/2 cm

Height of ΔBCA( OC) = 7 cm

Base of ΔBCA ( AB )= 14 cm

Area of ΔBCA = 1/2 × base × height

Area of ΔBCA = 1/2 × AB × OC = 1/2 × 7 × 14 = 49 cm²

Area of larger semicircle with radius (OA)7 cm = 1/2 ×π ×7²= 1/2 ×22/7 ×7×7 = 77 cm²

Area of smaller circle with radius 7/2 cm = πr²= 22/7 × 7/2 × 7/2 = 77/2 cm² 

Area of the shaded region =Area of smaller circle with radius 7/2 cm +Area of larger semicircle with radius 7 cm - Area of ΔBCA 

Area of the shaded region = 77/2 + 77 - 49= 77/2 + 28 = (77 +56) /2= 133/2

Area of the shaded region = 66.5 cm²

Answer 2

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