Pentagonal Pyramid Calculation

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.

Pentagonal Pyramid Calculator  Input Delete Entry Edge length Volume Surface area Height Decimal places 0 1 2 3 4 6   Results Edge length a Volume V Surface area S Height h

Formulas for a pentagonal pyramid

Volume

\(\displaystyle V=\frac{5+\sqrt{5}}{24}·a^3 \;\;\;\;≈ 0.3015 ·a^3\)

Surface area

\(\displaystyle S= \frac{a^2}{2}· \sqrt{\frac{5}{2}·\left(10+\sqrt{5}+\sqrt{75+30·\sqrt{5}}\right)} \) \(\displaystyle \;\;\;\;≈ 3.8855 ·a^2 \)

Height

\(\displaystyle h=\frac{5-\sqrt{5}}{10} · a\;\;\;\;≈0.5257 ·a \)