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

 

square with radius 16 ft.

 

 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 smiley

 Mar 16, 2021
edited by idyllic  Mar 16, 2021

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