Answer:
The area of the regular polygon i.e. regular hexagon with a side length of 85 is:
- [tex]A\approx 18771.10[/tex]
Step-by-step explanation:
By definition, all sides of a regular polygon are equal in length.
We consider the regular hexagon as our regular polygon, as show in attached figure.
As
side length = a = 85
Using formula to find the area of the regular polygon i.e. regular hexagon
[tex]A\:=\:\frac{3\sqrt{3}}{2}a^2[/tex]
[tex]A=\frac{3\sqrt{3}}{2}\left(85\right)^2[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]A=\frac{3\sqrt{3}\cdot \:85^2}{2}[/tex]
[tex]A=\frac{21675\sqrt{3}}{2}[/tex] ∵ [tex]3\sqrt{3}\cdot \:85^2=21675\sqrt{3}[/tex]
[tex]A\approx 18771.10[/tex]
Therefore, the area of the regular polygon i.e. regular hexagon with a side length of 85 is:
- [tex]A\approx 18771.10[/tex]
