Question

the pentagon below has an area of 8.3 square centimeters.
what is the approximate length of the apothem?
○ 0.4 cm
○ 0.8 cm
○ 1.5 cm
○ 1.9 cm

Explanation:

Step1: Recall regular polygon area formula

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

Step2: Calculate the perimeter

For a regular pentagon with side length $s=2.2$ cm, perimeter $P = 5s$.
$P = 5 \times 2.2 = 11$ cm

Step3: Rearrange formula to solve for $a$

Rearrange $A = \frac{1}{2} \times a \times P$ to isolate $a$: $a = \frac{2A}{P}$

Step4: Substitute values and compute

Substitute $A=8.3$ cm² and $P=11$ cm:
$a = \frac{2 \times 8.3}{11} = \frac{16.6}{11} \approx 1.5$ cm

Answer:

1.5 cm