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Tricky triangle brainteaser

By , 29 March 2023

Difficulty: Tricky

All of the triangles below are equilateral, meaning all of their sides have an equal length. If the purple shaded triangle has an area of 2, what is the area of the largest triangle?

A diagram of a triangle inside an upside down triangle inside a bigger triangle. The middle triangle is purple.

Scroll down or click for a hint, or the answer!

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Brainteaser hint

Can you find any other triangles that are the same size as the shaded triangle?

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Brainteaser answer

The best way to solve this puzzle is to work your way from the centre out. The 3 small triangles in the middle are all the same size as the shaded triangle, and so they each have an area of 2.

Together with the shaded triangle, these 4 make up a medium-sized triangle. It has an area of 4 x 2 = 8. And this triangle is exactly the same size as the other 3 medium triangles!

To calculate the area of the whole big triangle, we just need to add everything up.
8 + 8 + 8 + 8 = 32

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