Question

Question 16
Calculate the area of the designed region in figure common between the two quadrants of circle of radius 8 cm each.

Answer 1

AB = BC = CD = AD = 8 cm
Area of $\Delta ABC=Areaof\Delta ADC$
$=\frac{1}{2}\times 8\times 8=32c{m}^2$
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 $\Delta ABC)$ + (Area of quadrant AFCD - Area of $\Delta ADC)$
$=(\frac{352}{7}-32)+(\frac{352}{7}-32)c{m}^2$
$=2\times (\frac{352}{7}-32)c{m}^2$
$=\frac{256}{7}c{m}^2$