Two of a kind

The red and blue triangles are similar. The white areas are given. What is the total area?

Scroll down for a solution to this problem.


The total area is 8.

First we name the parallel sides as shown, using the similarity of the red and blue triangles. From the triangle area formula A=absin(α)/2, we deduce that the large triangle is x2A, but als that 2=xA.

Now from comparing the similar triangles with base b and xb, we get x2 =A+3. We have two equations with variables x and A. They can be solved to give A=1 and x=2, leading to a total area of 8.

🤞 Don’t miss these puzzles!

Subscribe to the weekly geometry puzzle e-mail.

Leave a Reply

Your email address will not be published. Required fields are marked *

Optionally add an image (JPEG only)