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How many triangles are there in a regular pentagon with all its diagonals drawn?

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How many triangles are there in a regular pentagon with all its diagonals drawn?

Note: a regular pentagon has five straight sides all of the same length and five equal angles. A diagonal is a line joining points.

posted Oct 23, 2017 by anonymous

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1 Answer

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enter image description here

A regular Pentagon with all its diagonals drawn will have 10 vertices { 5 inner and 5 outer vertices }. Now to draw a triangle we need exactly 3 vertices. So the answer to the question becomes 5 Choose 3 or 5C3 = 10 + (the triangles made by using 1 or more inner vertices) 15 = 35 which is also the number of triangles obtainable from the above figure.

answer Oct 25, 2017 by Tejas Naik



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