Tetracontágono

Predefinição:Info/Polígono Tetracontágono é uma forma de polígonos que tem 40 lados.

$\begin{array}{cc}A=10t^2\cot \frac{\pi }{40}=& 10(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}+\sqrt{{(1+\sqrt{5}+\sqrt{5+2\sqrt{5}})}^2+1})t^2\\ =& 10(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}+\sqrt{{(1+\sqrt{5})}^2+(\genfrac{}{}{0ex}{}{2}{1})(1+\sqrt{5})\sqrt{5+2\sqrt{5}}+{\left(\sqrt{5+2\sqrt{5}}\right)}^2+1})t^2\\ =& 10(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}+\sqrt{{(6+(\genfrac{}{}{0ex}{}{2}{1})\sqrt{5})}^{}+(\genfrac{}{}{0ex}{}{2}{1})(1+\sqrt{5})\sqrt{5+2\sqrt{5}}+{(5+2\sqrt{5})}^{}+1})t^2\\ =& 10(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}+\sqrt{(11+4\sqrt{5}+(\genfrac{}{}{0ex}{}{2}{1})(1+\sqrt{5})\sqrt{5+2\sqrt{5}})+1})t^2\\ =& 10(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}+\sqrt{12+4\sqrt{5}+(\genfrac{}{}{0ex}{}{2}{1})(1+\sqrt{5})\sqrt{5+2\sqrt{5}}})t^2\end{array}$