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Calculate the area of the designed region in the figure common between the two quadrants of the circles of the radius 8 cm each.
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 $\frac{256}{7} \mathrm{~cm}^{2}$.