Question

1. dean is building a gazebo with a floor shaped like a regular hexagon. the plans call for each side to be 10 feet long and the apothem is 8.66 feet. which is closest to the area of the floor? 519.6 square feet 259.8 square feet 86.6 square feet 60 square feet

Explanation:

Step1: Recall the formula for the area of a regular polygon

The formula for the area \( A \) of a regular polygon is \( A=\frac{1}{2} \times \text{perimeter} \times \text{apothem} \).

Step2: Calculate the perimeter of the regular hexagon

A regular hexagon has 6 equal sides. Each side is 10 feet, so the perimeter \( P = 6\times10=60 \) feet.

Step3: Substitute the values into the area formula

We know the apothem \( a = 8.66 \) feet and the perimeter \( P = 60 \) feet. Substituting into the formula \( A=\frac{1}{2}\times P\times a \), we get \( A=\frac{1}{2}\times60\times8.66 \).

Step4: Calculate the area

First, \( \frac{1}{2}\times60 = 30 \). Then, \( 30\times8.66 = 259.8 \) square feet.

Answer:

259.8 square feet