Question

In the given figure, ABCD is a square of side $7cm$ and $A,B,C,D$ are centres of equal circles which touch externally in pairs. The area of the shaded region is

• A. $115.5c{m}^2$
• B. $164.5c{m}^2$
• C. $66.5c{m}^2$
• D. $266.5c{m}^2$

Answer 1

The correct option is B $164.5c{m}^2$

Required shaded area$=$Area of square$+4\times$area of circles$-4\times$area of quadrant
$={\left(7\right)}^2+4\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}-4\times \frac{90}{360}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}=49+154-\frac{77}{2}=203-38.5=164.5c{m}^2$