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.$\left[ Use\ \pi =\frac{22}{7}\right]$ "
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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