Number of Triangles

Probability Level 3

Find the number of triangles which can be formed by intersecting diagnols of a 20-sided regular polygon.

569832 1456 3067890 2349810 136200 987435

Ashish Menon by Ashish Menon , 20, India

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2 solutions

Tom Engelsman
Nov 26, 2020

Nice explanation found here.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ashish Menon
Feb 4, 2016

No. of triangles with 3 diagnol endpoints = 1140
No. of triangles with 4 diagnol endpoints = 19380
No. of triangles with 5 diagnol endpoints = 77520
No. of triangles with 6 diagnol endpoints = 38160
Therefore, total no. of triangles = 1140 + 19380 + 77520 + 38160 = 136200 136200


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Nice problem. I think it might be clearer if the question asked for "the number of triangles formed by intersecting diagonals" of a 20-sided regular polygon, as discussed here .

Brian Charlesworth - 5 years, 4 months ago

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Nice suggestion. Thank u

Ashish Menon - 5 years, 4 months ago

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