Question

The roof of a gazebo is a regular hexagon with a side length of 4 feet and an apothem of 3.7 feet. What is the area of the roof to the nearest tenth?

Answer 1

44.4 feet

Step-by-step explanation:

The equation to finding the area of a regular polygon is:

`Area = (1)/(2)ap`

The 'a' is the apothem and the 'p' is the perimeter. Since the question contains the apothem and a side (which can be multiplied by how many sides there are) to make a perimeter.

A hexagon has 6 sides, and each side is 4 ft. 6 times 4 yields 24 ft. The apothem is 3.7 ft. Substitute them into the equation above:

`Area = (1)/(2)(3.7)(24)`

It would be easier to multiply the 3.7 and 24 before halving, so that will give you: 88.8. Then by halving, you will get 44.4.

The area of the roof is 44.4 feet.