Question

What is the area of a regular decagon with a side length of 6 meters? Round your answer to the nearest tenth, if necessary.

Answer 1

Given:

A regular decagon has a side length of 6 meters.

We need to determine the area of the regular decagon.

Area of the regular decagon:

The area of the regular decagon can be determined using the formula,

`A=(5)/(2) a^(2) \sqrt{5+2 √(5)}`

where a is the length of the side of the regular decagon.

Now, substituting a = 6 in the above formula, we get;

`A=(5)/(2) (6)^(2) \sqrt{5+2 √(5)}`

Simplifying the terms, we have;

`A=(5)/(2) (36) \sqrt{5+2 √(5)}`

`A=90 \sqrt{5+2 √(5)}`

`A=90 √(5+4.47)`

`A=90 √(9.47)`

`A=90(3.078)`

`A=277.02`

Rounding off to the nearest tenth, we get;

`A=277.0`

Therefore, the area of the regular decagon is 277.0 m²