Questions: Find the perimeter of a regular polygon with an interior angle of 108° and side length of 2 in.

Solution Steps

To find the perimeter of a regular polygon given an interior angle, we first need to determine the number of sides of the polygon. The formula for the interior angle of a regular polygon is \((n-2) \times 180^\circ / n = 108^\circ\), where \(n\) is the number of sides. Solve this equation to find \(n\). Once \(n\) is known, the perimeter can be calculated by multiplying the number of sides \(n\) by the side length.

To find the number of sides \( n \) of the regular polygon, we use the formula for the interior angle: \[ \frac{(n-2) \times 180}{n} = 108 \] Rearranging this equation gives: \[ (n-2) \times 180 = 108n \] \[ 180n - 360 = 108n \] \[ 72n = 360 \] \[ n = \frac{360}{72} = 5 \]

The perimeter \( P \) of a regular polygon is given by: \[ P = n \times \text{side length} \] Substituting the values we found: \[ P = 5 \times 2 = 10 \]

Final Answer