In the below figure, $ O A B C $ is a square of side $ 7 \mathrm{~cm} $. If $ O A P C $ is a quadrant of a circle with centre O, then find the area of the shaded region. (Use $ \pi=22 / 7 $ )"

Given:

\( O A B C \) is a square of side \( 7 \mathrm{~cm} \).

\( O A P C \) is a quadrant of a circle with centre O.

To do: 

We have to find the area of the shaded region.

Solution:

Length of the side of the square $=7\ cm$

Area of the square $= (7)^2$

$= 49\ cm^2$

Radius of the quadrant $= 7\ cm$

Therefore,

Area of the quadrant $=\frac{1}{4} \pi r^{2}$

$=\frac{1}{4} \times \frac{22}{7} \times 7^2$

$=\frac{77}{2}$

$=38.5 \mathrm{~cm}^{2}$

Area of the shaded region $=$ Area of the square $-$ Area of the quadrant

$=49-38.5$

$=10.5 \mathrm{~cm}^{2}$

The area of the shaded region is $10.5\ cm^2$.

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Updated on: 10-Oct-2022

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