Elementary Geometry for College Students (7th Edition)

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