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In the given figure, find the area of the shaded region.

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30.5 {cm}^{2}

3.5 {cm}^{2}

20.5 {cm}^{2}

10.5 {cm}^{2}

answer is A.

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Detailed Solution

Given,
length = 8cm and breath = 6 cm
Area of rectangle =8×6=48

{cm}^{2}

Now, area of circle

= π r^{2}

(Here r is the radius of the circle)
Let the diagonal of the rectangle s cm.

s^{2} = 6^{2} + 8^{2}

s^{2} = 36 + 64

s^{2} = 100

s = 10 cm

Now, BD = 10 cm.

∵

It is a rectangle.
So, BD = OB+OD
OB = 5 cm
Now, area of circle

= π r^{2}

\frac{= 22}{7} \times {(5)}^{2}

= \frac{22}{7} \times 25

= \frac{550}{7}

= 78.5 {cm}^{2}

Area of shaded region = circle’s area – triangle’s area

= 78.5 {cm}^{2} - 48 {cm}^{2}

= 30.5 {cm}^{2}

Correct option is 1.

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