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.

Asked by Pragya Singh | 1 year ago |  82

##### 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 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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