Question

The area of an equilateral triangle is $49\sqrt{3}c{m}^2$. Taking each angular point as centre, circles are drawn with 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} = 1.73.]

Answer 1

Let "a" be the side of equilateral triangle.

$\frac{\sqrt{3}{a}^2}{4}=49\sqrt{3}{a}^2=49\times 4=196a=\sqrt{196}=14cm$

Radius of circle $=\frac{14}{2}=7$ cm

Area of one sector $=\frac{\theta }{360}\times \pi r^2=\frac{60}{360}\times \pi \times 7^2=\frac{1}{6}\times 3.14\times 49=25.64c{m}^2$

Area of all the 3 sectors $=25.64\times 3=76.92c{m}^2$

Area of triangle not included in the circle = area of triangle- area of all the 3 sectors

$=49\sqrt{3}-76.92=84.77-76.92=7.85c{m}^2$