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In figure below, $ P Q R S $ is a square of side $ 4 \mathrm{~cm} $. Find the area of the shaded square."
Given:
\( P Q R S \) is a square of side \( 4 \mathrm{~cm} \).
To do:
We have to find the area of the shaded square.
Solution:
Let the side of the square $PQRS$ be $a$.
This implies,
$a= 4\ cm$
Area of the square $PQRS= a^2$
$= 4^2=16\ cm^2$
Radius of each of the four quadrants at the corners $r= 1\ cm$
Area of 4 quadrants $=4 \times \frac{1}{4} \pi r^{2}$
$=\pi r^{2}$
$=\pi \times 1^2$
$=\pi \mathrm{cm}^{2}$
Radius of the inner circle $=\frac{2}{2}$
$=1 \mathrm{~cm}$
This implies,
Area of the inner circle $=\pi r^{2}$
$=\pi \times 1^2$
$=\pi \mathrm{cm}^{2}$
Therefore,
Area of the shaded region of the square $=16-\pi-\pi$
$=(16-2 \pi) \mathrm{cm}^{2}$
The area of the shaded square is $(16-2 \pi) \mathrm{cm}^{2}$.
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