Pentagonal Pyramid Calculation
Calculator and formulas for calculating a regular pentagonal based pyramid
This function calculates the properties of a regular pentagonal pyramid.
To perform the calculation, enter the base length and the height of the pyramid. Then click the 'Calculate' button.
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Formulas for the pentagonal pyramid
Slant height (\(\small{s}\))
\(\displaystyle s = \sqrt{h^2 + \frac{a^2 · cot^2(\frac{π}{5} )}{4}} \)
Edge length (\(\small{b}\))
\(\displaystyle b =\sqrt{s^2 + \frac{a^2}{4}}\)
Base area (\(\small{A}\))
\(\displaystyle A = \frac{5 · a^2 }{ 4 · tan(\frac{π}{5}) } \)
Slant area (\(\small{A_s}\))
\(\displaystyle A_s = \frac{a · s }{ 2} \)
Lateral Surface (\(\small{A_L}\))
\(\displaystyle A_L = \frac{ 5 · a · s }{ 2} \)
Surface area (\(\small{S}\))
\(\displaystyle S = A+ A_L \)
Perimeter (\(\small{P}\))
\(\displaystyle P = 5 ·a \)
Volume (\(\small{V}\))
\(\displaystyle V = \frac{A · h}{3} \)
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