The perimeter of a triangle is 12 and its inradius is 1. What is the area of the triangle

beastrohit Nov 14, 2018

#1**+1 **

This is a little easier than you might realize

Let us call the sides AB, BC and AC

And call the center of the incircle O

So....we can divide the larger triangle into three separate triangles - AOB, BOC and AOC

The inradius of the incircle forms an altitude of each triangle since it is perpendicular to each side

So.....the area, A, of the larger triangle can be expressed as

A = (1/2) [ altitude * ( sum of the bases ) ] =

(1/2) [ (1) * perimeter ] =

(1/2) [ (1)(AB + BC + AC ) ] =

(1/2) [ 1 * 12 ] =

(1/2) [ 12] =

6 units^2

CPhill Nov 14, 2018