Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top
  1. if you join all the vertices of a heptagon, how many quadrilaterals will you get?
  2. How many heptagons can be drawn by joining the vertices of a polygon with 10 sides?
  3. A polygon has 20 diagonals,how many sides does it have ? Are there are formula showing relation between diagonal and no of sides of a polygon?

These two questions are similar. Any clues to help me solve the problem.

share|cite|improve this question
For 3., have you tried drawing different polygons and counting up the number of diagonals and looking for a pattern? – Gerry Myerson Sep 11 '12 at 7:17
up vote 2 down vote accepted
  1. You need to choose 4 vertices from 7 vertices of Heptagon. How do you do that?
  2. Same as 1, you need to select 7 out of 10.
  3. No of distance diagonals is n(n-3)/2; you can do this if you can get above 2.
share|cite|improve this answer
thanks for number 3 but i could not figure out 1 and 2, – pradip Sep 11 '12 at 7:57
Its simple combination problem, you need to select 4 out of 7, it 7C4. {as the order doesn't matter} – Ram Sep 11 '12 at 8:21
@sonam: Try reading this article. User33263 is suggesting (correctly) that you want $\binom74$ and $\binom{10}7$. – Brian M. Scott Sep 11 '12 at 8:30
But there will be many quadrilaterals that won't have vertices on the Heptagon. – Saurabh Sep 11 '12 at 8:33

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.