Question

A triangle ABC is divided into four regions by three lines parallel to BC. The lines divide AB into four segments.If the second largest region has area 225 what is the area of ABC?​

Answer 1

Method 2

Let B1C1, B2C2, B3C3, be the lines parallel to BC. Draw lines parallel to AB . This

produces 4 small congruent triangles and 6 small congruent parallelograms.

Drawing the diagonal from top left to bottom right in any parallelogram produces two triangles

that are congruent to the top triangle. Thus triangle ABC can be divided into 16 congruent

triangles. The region B3C3C2B2 has area 225 and consists of 5 of these triangles. Hence

225 = 5

16 × |ABC| and |ABC| = 16

5 × 225 = 720