Question

find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length of 7.7 meters. round to the nearest tenth.

Explanation:

Step1: Recall the formula for area of a regular polygon

The formula for the area $A$ of a regular polygon is $A=\frac{1}{2}aP$, where $a$ is the apothem and $P$ is the perimeter.

Step2: Calculate the perimeter $P$

The polygon has $n = 7$ sides and each side has length $s=7.7$ meters. The perimeter $P=ns$. So, $P = 7\times7.7=53.9$ meters.

Step3: Calculate the area $A$

We know $a = 8$ meters and $P=53.9$ meters. Substitute into the area formula: $A=\frac{1}{2}\times8\times53.9$.
$A = 4\times53.9=215.6$ square - meters.

Answer:

$215.6$