Question

determine how many diagonals each of the following polygons has. a. heptagon b. nonagon a. a heptagon has 14 diagonals. b. a nonagon has 27 diagonals. c. an 18 -gon has 135 diagonals. d. a n -gon has diagonals. (type an expression using n as the variable.)

Explanation:

Step1: Recall the diagonal - formula

The formula for the number of diagonals $d$ of an $n$-sided polygon is $d=\frac{n(n - 3)}{2}$. This is because from each of the $n$ vertices, we can draw $n-3$ diagonals (we can't draw a diagonal to itself and to the two adjacent vertices). But we have double - counted each diagonal, so we divide by 2.

Answer:

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