Question

A square is inserted inside a circle such that the corners of the square coincide with the circumference of the circle. If the diameter of the circle is d, the area of the shaded part is ____$c{m}^2$.

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Answer 1

We need to find the area of the shaded region.

By subtracting the area of the square from the area of the circle we will be able to find the area of the shaded region.

The area of the circle is given by, A= $\pi \times (\frac{d}{2}{)}^2$ (when d is given)

= $\frac{22}{7}\times (\frac{28}{2}{)}^2$

= 616$c{m}^2$

We need to find the of the side to find the area of the square, By applying Pythagoras Theorem we get,

$a^2+a^2=d^2$

$\Rightarrow a=\frac{d}{\sqrt{2}}$

= $\frac{28}{\sqrt{2}}$

Now, the area of the square using the equation, A = $a^2$

= ${\left(\frac{28}{\sqrt{2}}\right)}^2$

= 392$c{m}^2$

The Area of the shaded region is = Area of the Circle – Area of the Square

= 616 – 392 = 224$c{m}^2$

The area of the shaded region is 224$c{m}^2$