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How Many Triangles Are There

How Many Triangles Are There Solution - 23 May

Can you count the number of triangles in the given figure?

PS: Think hard as it is not easy as it seems.

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There are a total of 47 triangles.

Let us divide the triangles in this figure in three equal triangles (triangles formed by connecting outer side to the center of the circle) and then count the number in each category by taking two or more together.

At first, let us count the triangles that are in one part. There are 4 non-overlapping and 3 overlapping triangles. This means that the total triangles are 7 * 3 = 21.

Next, we pick up the triangles by taking two parts together. There are 8 such triangles. 8 * 3 = 24.

Lastly, the triangles by taking all 3 parts together, we find there are only 2 triangles.

21 + 24 + 2 = 47.