Question

the area of the regular hexagon is $10.4\\ \text{in.}^2$.
what is the measure of the apothem, rounded to the nearest tenth of an inch?
○ 1.3 in.
○ 1.7 in.
○ 2.0 in.
○ 3.4 in.

Explanation:

Step1: Recall area formula for regular polygon

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

Step2: Calculate perimeter of hexagon

A regular hexagon has 6 sides, each 2 in.
\( p = 6 \times 2 = 12 \text{ in} \)

Step3: Rearrange formula to solve for apothem

Rearrange \( A = \frac{1}{2}pa \) to isolate \( a \):
\( a = \frac{2A}{p} \)

Step4: Substitute values and compute

Substitute \( A = 10.4 \text{ in}^2 \) and \( p = 12 \text{ in} \):
\( a = \frac{2 \times 10.4}{12} = \frac{20.8}{12} \approx 1.7 \text{ in} \)

Answer:

1.7 in.