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,
[tex]A=\frac{5}{2} a^{2} \sqrt{5+2 \sqrt{5}}[/tex]
where a is the length of the side of the regular decagon.
Now, substituting a = 6 in the above formula, we get;
[tex]A=\frac{5}{2} (6)^{2} \sqrt{5+2 \sqrt{5}}[/tex]
Simplifying the terms, we have;
[tex]A=\frac{5}{2} (36) \sqrt{5+2 \sqrt{5}}[/tex]
[tex]A=90 \sqrt{5+2 \sqrt{5}}[/tex]
[tex]A=90 \sqrt{5+4.47}[/tex]
[tex]A=90 \sqrt{9.47}[/tex]
[tex]A=90(3.078)[/tex]
[tex]A=277.02[/tex]
Rounding off to the nearest tenth, we get;
[tex]A=277.0[/tex]
Therefore, the area of the regular decagon is 277.0 m²
