## How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

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### How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

by sambati » Tue Aug 04, 2020 1:54 pm

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How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

A 35
B 40
C 50
D 65
E 70

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### Re: How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

by [email protected] » Wed Aug 05, 2020 12:20 am
sambati wrote:
Tue Aug 04, 2020 1:54 pm
How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

A 35
B 40
C 50
D 65
E 70
• Number of triangles can be formed from a polygon with 7 sides = 7C3 = (7*6*5) / (1*2*3) = 35;

• Number of quadrilaterals can be formed from a polygon with 7 sides = 7C4 = (7*6*5*4) / (1*2*3*4) = 35;

Total Number of ways that triangles and rectangles can be formed from a polygon with 7 sides = 35 + 35 = 70.

Hope this helps!

-Jay
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### Re: How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

by [email protected] » Mon Aug 10, 2020 3:28 am
sambati wrote:
Tue Aug 04, 2020 1:54 pm
How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

A 35
B 40
C 50
D 65
E 70
Solution:

There are 7C3 = (7 x 6 x 5) / (3 x 2) = 35 ways to choose 3 vertices from the 7 vertices of the polygon to form a triangle. Likewise, there are 7C4 = (7 x 6 x 5 x 4)/(4 x 3 x 2) = 35 ways to choose 4 vertices from the 7 vertices of the polygon to form a quadrilateral. Therefore, there is a total of 35 + 35 = 70 triangles and quadrilaterals that can be formed.