Question

a regular heptagon has an apothem of approximately 7.3 ft and a perimeter of approximately 49.0 ft. find the area of the heptagon.

Explanation:

Step1: Recall area formula for regular polygon

The area $A$ of a regular polygon is given by $A = \frac{1}{2} \times \text{apothem} \times \text{perimeter}$

Step2: Substitute given values

Substitute apothem $= 7.3$ ft and perimeter $= 49.0$ ft into the formula:
$A = \frac{1}{2} \times 7.3 \times 49.0$

Step3: Calculate the product

First compute $7.3 \times 49.0 = 357.7$, then multiply by $\frac{1}{2}$:
$A = \frac{357.7}{2} = 178.85$

Answer:

178.85 ft²