Question

a circle is inscribed in an equilateral triangle. which of the following is nearest the percent of the triangle's area occupied by the circle?
A 40%
B 50%
C 60%
D 70%
E 70%

Answer 1

say the side of equilateral triangle is \(a\)

Answer 2

use below fact of equilateral triangle :
altitude = median

Answer 3

The area of the triangle is therefore 3(sqrt(3)r)r=3sqrt(3)r^2
This will help you find the percentage.