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
How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?
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- Jay@ManhattanReview
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• 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.
Correct answer: E
Hope this helps!
-Jay
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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.
Answer: E
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