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.

## Solution

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 x^{2}A, but als that 2=xA.

Now from comparing the similar triangles with base b and xb, we get x^{2} =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.