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

we know every equilateral triangle makes all angles 60 degree
now first find side of triangle ,
area of triangle =root3/4 x (side length)^2
196root3=root3/4 x (side length)^2
side length =root {196 x 4 } =28 m

now according to question
radius of circular part =28/2 =14m
area of each circular part =pi.r^2/6
=22/7 x 14 x 14 x 1/6
=308/3 m^2
total area of circular part = 3 x area of each circular part =3 x 308/3 =308 m^2

hence area of remaining part of triangle
=(196root3-308)m^2