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natbricker13
natbricker13 natbricker13
  • 25-03-2015
  • Mathematics
Answered

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

Verified Answer :

konrad509
konrad509 konrad509
  • 25-03-2015

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


\(\alpha=\dfrac{(n-2)\cdot180}{n}\\\\ \alpha=\dfrac{(20-2)\cdot180}{20}\\ \alpha=\dfrac{18\cdot180}{20}\\ \alpha=162\)

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