Question

16. Calculate the area of the designed region in
Fig. 12.34 common between the two quadrants
of circles of radius 8 cm each.​

Answer 1

Area of shaded region =2× Area of segment BD

Considering the quadrant ABD,

Area of quadrant ABD=

$\frac{π \times {r}^{2} }{4} = \frac{1}{4} \times 3.14×8×8=50.24 {cm}^{2}$

Area of △ABD =

$\frac{1}{2} \times 8 \times 8 = {32cm}^{2}$∴ Area of segment BD = Area of quadrant ABD − Area of △ABD

=50.24−32=18.24cm²

∴ Area of shaded region =2×18.24=36.48cm²