Question

a regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.
what is the area of the pentagon, rounded to the nearest tenth?
○ 13.8 cm²
○ 17.3 cm²
○ 32.7 cm²
○ 69.0 cm²

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 $= 3$ cm and perimeter $= 21.8$ cm into the formula:
$A = \frac{1}{2} \times 3 \times 21.8$

Step3: Calculate the area

First compute $3 \times 21.8 = 65.4$, then $\frac{1}{2} \times 65.4 = 32.7$

Answer:

32.7 $\text{cm}^2$ (Option: 32.7 cm²)