Question

the area of the regular hexagon is 169.74 ft². what is the perimeter, rounded to the nearest tenth? 24.2 ft 28.3 ft 48.5 ft 56.8 ft

Explanation:

Step1: Recall area - perimeter relationship

The area formula for a regular polygon is $A=\frac{1}{2}ap$, where $A$ is the area, $a$ is the apothem, and $p$ is the perimeter. For a regular hexagon, the apothem is given as $a = 7$ ft and $A=169.74$ ft².

Step2: Solve for the perimeter

We can re - arrange the formula $A=\frac{1}{2}ap$ to solve for $p$. Multiply both sides of the equation by $2$ to get $2A = ap$. Then $p=\frac{2A}{a}$.
Substitute $A = 169.74$ ft² and $a=7$ ft into the formula: $p=\frac{2\times169.74}{7}$.
First, calculate $2\times169.74 = 339.48$. Then $\frac{339.48}{7}=48.497\approx48.5$ ft.

Answer:

48.5 ft