Question

How many triangles can be found in a polygon with 7 sides?

Answer 1

Answer:

287 triangles are found

Answer 2

Answer:

Number of triangles in a polygon with 7 sides $=35$.

Step-by-step explanation:

A polygon with 7 sides have 7 vertices.  Any 3 of the vertices will form a triangle.

Therefore, number of triangles = nCr, where n = 7 and r = 3

$\frac{n!}{r!(n-r)!}$

$=\frac{7!}{3!(7-3)!}$

$=\frac{7*6*5*4!}{3!*4!}$

$=\frac{7*6*5}{3!}$

$=\frac{7*6*5}{6}$

$=35$