Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 8 - Section 8.5 - More Area Relationships in the Circle - Exercises - Page 378: 9


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
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