Question

Calculate the area of the designed region in Fig. common between the two quadrants of circles of radius $8cm$ each.

Answer 1

$AB=BC=CD=AD=8cm$

$ar\left(∆ABC\right)=ar\left(∆ADC\right)$

Area of triangle$=\frac{1}{2}\times 8\times 8$

$=32c{m}^2$

Area of quadrant $AECB=$Area of quadrant $AFCD=\frac{1}{4}\times \frac{22}{7}\times 8^2$

$=\frac{352}{7}c{m}^2$

Area of shaded region = (Area of quadrant $AECB$ $-$ Area of $\left(∆ABC\right)$ $=$ (Area of quadrant $AFCD$ – Area of $\left(∆ADC\right)$

$$\begin{gathered} =\left(\frac{352}{7}-32\right)+\left(\frac{352}{7}-32\right)c{m}^2 \\ =2\times \left(\frac{352}{7}-32\right)c{m}^2 \\ =\frac{256}{7}c{m}^2 \\ =36.57c{m}^2 \end{gathered}$$

Hence , the required value is $36.57c{m}^2$.