How to transform quadrilaterals into triangles with the same area

Quadrilaterals have four sides. To make triangles out of them, three of the vertices should be collinear. Now, what construction should you make so that the area remain unchanged? Here’s how you can transform quadrilaterals into triangles with the same are in three easy steps.

1. Extend one of the sides of the quadrilateral. Let’s extend AB in the figure below.

2. Construct a line parallel through one of the diagonals of the quadrilateral. In our example, let’s use diagonal BD.

3. Draw the triangle.

Can you figure out why the constructions produce a triangle equal in area to the quadrilateral?

Challenge Problem

I suggest you try solving the problem first before clicking in the link.

Transform a pentagon into a triangle without changing its area.

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