Pentagonal Pyramid Calculation
Calculators and formulas for a pentagonal pyramid (Johnson solid J2)
The pentagonal pyramid has a regular pentagon as its base. The sides of the pyramid are bounded by five equilateral triangles. All edges have the same length. The pentagonal pyramid is one of the Johnson solids (J2).
To perform the calculation select the property you know from the menu and enter its value. Then click on the 'Calculate' button.
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Pentagonal Pyramid Formulas
Volume (\(\small{V}\))
\(\displaystyle V=\frac{5+\sqrt{5}}{24}·a^3 \;\;\;\;≈ 0.3015 ·a^3\)
Surface area (\(\small{S}\))
\(\displaystyle S= \frac{a^2}{2}· \sqrt{\frac{5}{2}·\left(10+\sqrt{5}+\sqrt{75+30·\sqrt{5}}\right)} \) \(\displaystyle \;\;\;\;≈ 3.8855 ·a^2 \)
Height (\(\small{h}\))
\(\displaystyle h=\frac{5-\sqrt{5}}{10} · a\;\;\;\;≈0.5257 ·a \)
Square Pyramid • Pentagonal Pyramid • Triangular Cupola • Square Cupola • Pentagonal Cupola • Rotunda • Elongated Triangular Pyramid • Elongated Square Pyramid • Elongated Pentagonal Pyramid • Triangular Bipyramid • Pentagonal Bipyramid • Elongated Square Bipyramid • Gyrobifastigium • Gyroelongated Square Dipyramid • Snub Disphenoid
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