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Puzzle: Count the Number of Triangle in the following Pentagon?

+2 votes
1,857 views

Count the number of triangles in the following figure i.e. Connected Pentagon?

Pentagon

posted Jan 21, 2014 by Luv Kumar

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Looks to be 35 (10+10+10+5)

1 Answer

+1 vote

It is 35.

Logic:

Lets count the number of triangles where side of the pentagon is one of the side of the triangle, for each one such side there are 6 triangles. but two of triangle has other side of the pentagon, those will be counted twice so we will count only one triangle for each side, so for five sides, total 5*5 = 25 such triangles.

Now, lets count the triangles where side of the pentagon is not the side of the triangle: there are 5+5 = 10 such triangles, this will be clear by the below diagram(5 green and 5 red triangles).

Thus, there are a total of 25+ 10= 35 triangles

answer Jan 21, 2014 by Atul Mishra
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