Online calculator and formulas for calculating a pentagon
This function calculates various parameters of a regular pentagon, a polygon with 5 vertices. Enter one of the known parameters for the calculation.
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Circumference \(P\) |
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\(\displaystyle P = a · 5 \) |
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Area \(A\) |
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\(\displaystyle A =\frac{a^2}{4} · \sqrt{25+10 · \sqrt{5}} \) |
\(\displaystyle ≈\frac{a^2}{4} ·6.88191 \) |
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Height \(h\) |
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\(\displaystyle h = ra+ri\) |
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\(\displaystyle h =\frac{a}{2} · \sqrt{5 +2· \sqrt{5}} \) |
\(\displaystyle ≈\frac{a}{2} · 3.07768 \) |
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Calculate Diagonal \(d\) |
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\(\displaystyle d = \frac{a}{2} ·(1+ \sqrt{5 }) \) |
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Circumcircle radius \(ra\) |
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\(\displaystyle ra = \frac{a}{2·cos(β)}\) |
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\(\displaystyle ra = \frac{a}{2·cos(54)}\) |
\(\displaystyle ≈\frac{a}{ 1.17557}\) |
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Incircle radius \(ri\) |
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\(\displaystyle ri= \sqrt{ra^2-a^2}\) |
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Edge length \(a\) |
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\(\displaystyle a = \frac{ h · 2}{ \sqrt{5+2·\sqrt{5}}} \) |
\(\displaystyle ≈ \frac{ h · 2}{ 3.07768} \) |
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\(\displaystyle a = \sqrt{ \frac{ A · 4}{ \sqrt{25+10·\sqrt{5}}} } \) |
\(\displaystyle ≈ \sqrt{ \frac{ A · 4}{6.88191} } \) |
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\(\displaystyle a = \frac{P}{5}\) |
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