Calculate the area of the designed region in the figure common between the two quadrants of the circles of the radius 8 cm each.
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Given:

Side of the square $= 8\ cm$

Radius of the quadrant $= 8\ cm$

To do:

We have to calculate the area of the designed region in the figure.

Solution:

Side of the square $= 8\ cm$
Area of the square $= 8^2$

$= 64\ cm^2$

Radius of the quadrant $= 8\ cm$

Area of the quadrant $=\frac{\pi r^{2} \theta}{360^{\circ}}$

$=\frac{22}{7} \times \frac{8 \times 8 \times 90^{\circ}}{360^{\circ}}$

$=\frac{22 \times 2 \times 8}{7}$

$=\frac{352}{7}$

Area of the square left on subtracting area of one quadrant $=$ Area of the square $-$ Area of the quadrant

$=64-\frac{352}{7}$

$=\frac{448-352}{7}$

$=\frac{96}{7} \mathrm{~cm}^{2}$

Area of the shaded region $=$ Area of the square $-2 \times$ Area of the square left on subtracting area of one quadrant

$=64-2 \times \frac{96}{7}$

$=\frac{448-192}{7}$

$=\frac{256}{7} \mathrm{~cm}^{2}$

The area of the designed region is $\frac{256}{7} \mathrm{~cm}^{2}$.

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Updated on: 10-Oct-2022

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