Question

a regular octagon has a side of approximately 6.0 cm and an apothem of approximately 7.2 cm. find the area of the octagon.

Explanation:

Step1: Calculate perimeter of octagon

An octagon has 8 sides, so perimeter $P = 8 \times 6.0 = 48.0$ cm

Step2: Use area formula for regular polygon

The area $A$ of a regular polygon is $\frac{1}{2} \times P \times a$, where $a$ is the apothem.
Substitute values: $A = \frac{1}{2} \times 48.0 \times 7.2$

Step3: Compute final area

First calculate $\frac{1}{2} \times 48.0 = 24.0$, then $24.0 \times 7.2 = 172.8$

Answer:

$172.8$ $\text{cm}^2$