Question

In Fig, arcs are drawn by taking vertices $A,B$ and $C$ of an equilateral triangle of side $10cm$. to intersect the sides $BC,CA$ and $AB$ at their respective mid-points $D,E$ and $F$. Find the area of the shaded region (Use $\pi =3.14$).

• A. $13.08$ $c{m}^2$
• B. $39.25$ $c{m}^2$
• C. $33.25$ $c{m}^2$
• D. $89.25$ $c{m}^2$

Answer 1

The correct option is B $39.25$ $c{m}^2$

Sectors made at vertices $A,B,C$ are equal in Area because angle made by them is equal to ${60}^0$ and radius of each circle is $\frac{10}{2}cm=5cm$

Area of shaded region $=3\times$ Area of one sector with radius $5cm$ and angle ${60}^0$

$=3\times \frac{60}{360}\pi (5{)}^2{cm}^2$

$=39.25{cm}^2$