#### Answer

A = $\frac{3}{2}$rs

#### Work Step by Step

Given a circle of radius r is inscribed in an equilateral triangle whose sides have length s
We need to find an expression for the area of the triangle in terms of r
and s.
Where P represents the perimeter of a triangle and r represents the length of the radius of its inscribed circle, the area of the triangle is given by
A = $\frac{1}{2}$rP
Perimeter of triangle = s+s+s = 3s for equilateral triangle
A = $\frac{1}{2}$r* 3s
A = $\frac{3}{2}$rs