# Mock AIME I 2012 Problems/Problem 3

## Problem

Triangle has , , . The trisection points of are and , with . Segments and are extended to points and such that and . The area of pentagon is , where and are relatively prime positive integers. Find .

## Solution

Use Heron's formula to find . Also note from the trisection that . Now . Similarly, . From this we deduce that

(i)

(ii) Similarly to (i),

(iii) with ratio , so

The area of our pentagon is . The answer is .