Question

a regular pentagon has an apothem measuring 20 cm and a perimeter of 145.3 cm. what is the area of the pentagon? square centimeters

Explanation:

Step1: Recall area formula for regular polygon

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

Step2: Substitute given values

Substitute perimeter $= 145.3$ cm and apothem $= 20$ cm into the formula:
$A = \frac{1}{2} \times 145.3 \times 20$

Step3: Calculate the result

First simplify $\frac{1}{2} \times 20 = 10$, then compute $145.3 \times 10 = 1453$

Answer:

1453 square centimeters