In fig OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with center O, then find the area of the shaded region.$\left[ Use\ \pi =\frac{22}{7}\right]$
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Given: Side of the square OABC$=7$ cm. A quadrant OAPC of a circle with center O.

To do: To find the area of the shaded region.

Solution:  Here OA is the side of the given square,

$\therefore\ OA=7\ cm$
 Area of the square OABC$=( side)^{2}$

$=7^{2}$

$=49\ cm^{2}$

Here OA is the radius of the quadrant OAPC, 

$r=7\ cm$

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

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

$=\frac{77}{2} \ cm^{2}$

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

$=49-\frac{77}{2}$

$=49-38.5$

$=10.5\ cm^{2}$

Therefore, Area of the shaded region is $10.5\ cm^{2}$.

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Updated on: 10-Oct-2022

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