natbricker13 natbricker13

25-03-2015
Mathematics

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What is the area of a 20 sided regular polygon with a side length of 10 (for each side).

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konrad509 konrad509

25-03-2015

[tex]A=5a^2(1+\sqrt5+\sqrt{5+2\sqrt5})\\ A=5\cdot10^2\cdot(1+\sqrt5+\sqrt{5+2\sqrt5})\\ A=500(1+\sqrt5+\sqrt{5+2\sqrt5})\\ A\approx3157[/tex]

[tex]\alpha=\dfrac{(n-2)\cdot180}{n}\\\\ \alpha=\dfrac{(20-2)\cdot180}{20}\\ \alpha=\dfrac{18\cdot180}{20}\\ \alpha=162[/tex]

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