Question

Find the area of the shaded region, where the side of square ABCD is $10$cm and two arcs are drawn from two opposite vertices of the square.

• A. $\frac{200}{7}$sq. unit
• B. $\frac{400}{7}$sq. unit
• C. $\frac{600}{7}$sq. unit
• D. $\frac{100}{7}$sq. unit

Answer 1

The correct option is B $\frac{400}{7}$sq. unit

Area of shaded region

$=2$[Area of quadrant $-$ Area of triangle]

$=2\left[\frac{\pi (10{)}^2}{4}-\frac{1}{2}\times 10\times 10\right]$

$=2\times 100\left[\frac{22}{7\times 4}-\frac{1}{2}\right]$

$=200\times \frac{2}{7}=\frac{400}{7}$Sq.cm.