Question

The area of equilateral triangle is 196 root 3 meter sq..three circles are drawn at the vertices of the triangle with radius egalitarian to the half of the side of triangle. Find the area of triangle not included in the sectors.

Answer 1

The area of an equilateral Δ = √3 a ²/4
 ⇒196 √3 = √3 a² /4
 ⇒a = 14
Therefore,r = a/2
                   = 28/2  = 14 m

We have to find the area of blue region
Therefore,
The area of Δ - area of three sectors (with r= 14 m and Ф = 60° )
⇒196 √3 - [3 (Ф$\pi$r²/360)]
⇒339.47 - (180 $\pi$ * 14 * 14/360)
⇒339.47 - 308
⇒ 31.47 m ²