Answer: approximately 4478.46096908264 square cm.
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Explanation:
I'm assuming this is a regular 12-sided polygon
The area formula for regular polygons is
[tex]A = 0.25n*s^2*\cot(180/n)[/tex]
where in this case we have n = 12 sides and each side is of length s = 20
So,
[tex]A = 0.25n*s^2*\cot(180/n)\\\\A = 0.25*12*(20)^2*\cot(180/12)\\\\A = 0.25*12*(20)^2*\cot(15)\\\\A = 0.25*12*(20)^2*\frac{1}{\tan(15)}\\\\A \approx 4478.46096908264\\\\[/tex]
The area of this regular polygon is approximately 4478.46096908264 square cm.
Make sure your calculator is in degree mode when computing that value of cot(15) or 1/tan(15).
