Question

What is the number of diagonals that intersect at a given vertex of a hexagon, heptagon, 30-gon and n-gon?

Answer 1

Answer:

i. 9

ii. 14

iii. 405

iv. $\frac{n(n-3)}{2}$

Step-by-step explanation:

The number of diagonals in a polygon of n sides can be determined by:

$\frac{n(n-3)}{2}$

where n is the number of its sides.

i. For a hexagon which has 6 sides,

number of diagonals = $\frac{6(6-3)}{2}$

                                   = $\frac{18}{2}$

                                   = 9

The number of diagonals in a hexagon is 9.

ii. For a heptagon which has 7 sides,

number of diagonals = $\frac{7(7-3)}{2}$

                                   = $\frac{28}{2}$

                                   = 14

The number of diagonals in a heptagon is 14.

iii. For a 30-gon;

number of diagonals = $\frac{30(30-3)}{2}$

                                          = $\frac{810}{2}$

                                         = 405

The number of diagonals in a 30-gon is 405.

iv. For a n-gon,

number of diagonals = $\frac{n(n-3)}{2}$

The number of diagonals in a n-gon is $\frac{n(n-3)}{2}$