Question

The area of an equilateral triangle is 49$\sqrt{3}{cm}^2$ . Taking each angular point as the centre, circles are drawn with a radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles.(Take $\sqrt{3}=1.732)$

Answer 1

Area of triangle is $49\sqrt{3}c{m}^2$

$\frac{\sqrt{3}}{4}{a}^2=49\sqrt{3}⟹a=14cm$

The area of $3$ circles is

$=3\frac{\theta }{360}\times \pi r^2=3\times \frac{60}{360}\times \frac{22}{7}\times 7\times 7=77c{m}^3$

Area of remaining part is

$49\sqrt{3}-77=84.868-77=7.868c{m}^2$