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Question

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

Hint:

### Use area of semi-circle OACB to find area of shaded region. Also, note that ABC is forming a triangle.

## The correct answer is: 66.395 cm2

### It is given that OA = 7 cm

i.e. Radius of bigger circle = 7 cm

Area of shaded region = Area of smaller circle + Area of semi-circle OACB – Area of triangle ABC

Now, OD is radius of bigger circle and diameter of smaller circle

i.e. radius of smaller circle = half of radius of bigger circle

r_{1} = 3.5 cm

Area of smaller circle = (r_{1})^{2}

= 3.14 × (3.5)^{2} = 38.465 cm^{2}

Area of semi-circle OACB = × r^{2}

= × 3.14 × 7^{2} = 76.93 cm^{2}

AB = diameter of bigger circle = 2 × 7 = 14 cm

OC = radius of bigger circle = 7 cm

Area of triangle ABC = × b × h = × AB × OC

= × 14 × 7 = 49 cm^{2}

Now, Area of shaded region = Area of smaller circle + Area of semi-circle OACB – Area of triangle ABC

= 38.465 cm^{2} + 76.93 cm^{2} - 49 cm^{2}

= 66.395 cm^{2}

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