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Bunuel
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I think this is a high-quality question and I agree with explanation.
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I think this is a high-quality question and I agree with explanation.
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I think this is a high-quality question and I agree with explanation.
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What happens if instead of a 7-sided regular polygon, we have a 6-sided, 8-sided or 20-sided regular polygon, how does having colinear vertices impact on the reasoning for this question?
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nicorabinovich
What happens if instead of a 7-sided regular polygon, we have a 6-sided, 8-sided or 20-sided regular polygon, how does having colinear vertices impact on the reasoning for this question?
If you replace the 7-sided regular polygon with a 6-, 8-, or 20-sided regular polygon, the logic still holds exactly the same, because in any regular polygon, no three vertices are colinear.

That’s the key reason we can safely say:

  • Any 3 chosen vertices will always form a triangle.
  • Any 4 chosen vertices will always form a quadrilateral.

So the reasoning applies to any regular polygon with n ≥ 3, regardless of how many sides it has. Colinearity would only be a problem if three or more points lay on a straight line, which does not happen in regular polygons.
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I like the solution - it’s helpful.
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What a nice and tough question..... a lot of us like me will go down the memory lane and think of it as one of the questions we used to do in a childhood...Where we used to find the the no of triangles in a given figure......Where several triangles were there inside a triangles.......Eg...attached below....BUT its not that...the questions says vertices of a 7 sided regular polygon...So just pick the vertices and then its pretty easy..!!!


Bunuel
How many total triangles and quadrilaterals can be created using the vertices of a 7-sided regular polygon? (A regular polygon is a polygon with equal sides and angles.)

A. 35
B. 40
C. 50
D. 65
E. 70

Attachments

xhow-many-triangles-are-there-in-this-figure.jpg.pagespeed.ic.hYO73kirfS.jpg
xhow-many-triangles-are-there-in-this-figure.jpg.pagespeed.ic.hYO73kirfS.jpg [ 6.57 KiB | Viewed 86 times ]

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I like the solution - it’s helpful. I got the 35, 35. But I went by the word AND. so it becomes 35 X 35. Can you explain why OR has been applied here to make it 35 + 35?
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padmru
I like the solution - it’s helpful. I got the 35, 35. But I went by the word AND. so it becomes 35 X 35. Can you explain why OR has been applied here to make it 35 + 35?

This has already been addressed in the thread. Please review.
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I like the solution - it’s helpful.
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