A regular 15-gon has a perimeter of 150 m. To the nearest tenth, what is the area of the figure?

I know the answer is 1764.2 cm squared, but I don't know how to get there.

Question

A regular 15-gon has a perimeter of 150 m. To the nearest tenth, what is the area of the figure?

I know the answer is 1764.2 cm squared, but I don't know how to get there.

compassionate · Answer

Is it a regular polygon?

anonymous · Answer

Yes.

compassionate · Answer

So take 15/150 and it will give you your sides to setup the equation.

compassionate · Answer

150/15

anonymous · Answer

So each side is 10 cm

compassionate · Answer

Right! So $$A = \frac{ ns^2 \cot \frac{ 180 }{ n }  }{ 10 }$$

compassionate · Answer

There should be a degree symbol before "cot" but I couldn't do it

anonymous · Answer

Cot is cotanjent, correct? I'm only in high school  geometry so we haven't really gone over trig very much. Is there any other way to do it? I'm not sure if my teacher will let me get away with that.