Ab and cd are two diameters of a circle

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In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

Answered by admin @


[fig. is in the attachment]


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

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Hope this will help you....

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