Question

how many diagonals does a heptagon have?
______ diagonals

question 11
how many distinct diagonals does a nonagon have?
______ diagonals

Explanation:

Step1: Recall the formula for the number of diagonals in a polygon

The formula for the number of diagonals \(d\) in an \(n -\)sided polygon is \(d=\frac{n(n - 3)}{2}\).

Step2: Find the number of diagonals in a heptagon

For a heptagon, \(n = 7\). Substitute \(n=7\) into the formula: \(d=\frac{7\times(7 - 3)}{2}=\frac{7\times4}{2}=14\).

Step3: Find the number of diagonals in a nonagon

For a nonagon, \(n = 9\). Substitute \(n = 9\) into the formula: \(d=\frac{9\times(9 - 3)}{2}=\frac{9\times6}{2}=27\).

Answer:

Heptagon: \(14\) diagonals
Nonagon: \(27\) diagonals