In the given figure, AB and CD are two diameters of a circle (with center 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.

In fig., 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 = 14

Asked by Pragya Singh | 1 year ago |  82

1 Answer

Solution :-

Radius of larger circle, R = 7 cm

Radius of smaller circle, r = \( \dfrac{7}{2}\) cm

Height of ΔBCA = OC = 7 cm

Base of ΔBCA = AB = 14 cm

Area of ΔBCA = \( \dfrac{1}{2}\) × AB × OC = (\( \dfrac{1}{2}\))×7×14 = 49 cm2

Area of larger circle = πR= (\( \dfrac{22}{7}\))×72 = 154 cm2

Area of larger semicircle = \( \dfrac{154}{2}\) cm= 77 cm2

Area of smaller circle = πr2 = \( \dfrac{22}{7}\times \dfrac{7}{2}\times \dfrac{7}{2}=\dfrac{77}{2} \) cm2

Area of the shaded region 

= Area of larger circle – Area of triangle – Area of larger semicircle + Area of smaller circle

Area of the shaded region = (154-49-77+\( \dfrac{77}{2}\)) cm2

\( \dfrac{133}{2}\) cm2 = 66.5 cm2

Answered by Abhisek | 1 year ago

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