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# geometry

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Find the area of the regular polygon.  Give the answer to the nearest tenth.

Mar 16, 2021

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if the "radius" of the square is $$16$$ feet, then the length of the diagonal of the square would be $$16 \cdot 2 = 32$$ feet.

because of right triangle properties, $$32 = \sqrt2 \cdot s$$, where $$s$$ is the side length of the square. so, dividing $$\sqrt{2}$$ from both sides, we get

$$\frac{32}{\sqrt2} = s$$

the area of a square is just $$s^2$$, so the area of this square would be $$(\frac{32}{\sqrt2})^2$$ = $$\frac{32^2}{\sqrt2^2}$$ = $$\frac{1024}{2}$$ = $$512$$.

hope this helped! please let me know if you have any further questions

Mar 16, 2021
edited by idyllic  Mar 16, 2021