Question

Find the area of the shaded part in the figure shown, where ABCD is a square, region I is semicircle on CD as diameter, region II and III are quadrants of circles with centres at A and B respectively each having radius $7cm$.

Answer 1

Area of shaded region = Area of square ABCD - Area of region I - Area of region II - Area of region III

Now,

Area of square = $14\times 14=196c{m}^2$

Area of region I = $\frac{1}{2}\times \frac{22}{7}\times 7^2=77c{m}^2$

Area of region II = Area of region III = $\frac{1}{4}\times \frac{22}{7}\times 7^2=\frac{77}{2}c{m}^2$

Therefore,

Required area = $(196-77-77)c{m}^2=42c{m}^2$