Find the area of the regular polygon. Give the answer to the nearest tenth.
square with radius 16 ft.
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 \((\frac{32}{\sqrt2})^2\) = \(\frac{32^2}{\sqrt2^2}\) = \(\frac{1024}{2} \) = \(512\).
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