How to transform a pentagon into a triangle of the same area

This is the third in the series of problems involving transforming polygons into another polygon where the area is preserved. The first is about transforming a shape into another shape of the same area and the second is about transforming a quadrilateral into a triangle of the same area. The following problem builds on the first two problems. This doesn’t mean that you cannot solve the problem below without checking on the first two problems first.

Problem

Transform pentagon ABCDE into a triangle that has the same area as the pentagon.

Solution

The area of pentagon ABCDE is equal to the area of quadrilateral AFDE

Constructing the triangle from the quadrilateral is left to you as an exercise. If you are having some difficulty trying to understand the solution I suggest you read the two earlier problems:

• How to transform quadrilaterals into triangles with the same area
• Transforming shapes without changing their areas