Elongated Pentagonal Pyramid

The elongated pentagonal pyramid has an equilateral pentagon as its base. The sides are bounded by 5 equilateral triangles and 5 squares. All edges have the same length. The elongated pentagonal pyramid is one of the Johnson solids (J₉).

To perform the calculation select the property you know from the menu and enter its value. Then click on the 'Calculate' button.

Elongated 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 Elongated Pentagonal Pyramids

Volume

\(\displaystyle V= \frac{5+\sqrt{5}+6·\sqrt{25+10·\sqrt{5}}}{24}·a^3\) \(\displaystyle \;\;\;\;≈ 2.022 ·a^3\)

Surface area

\(\displaystyle S= \frac{20+5·\sqrt{3}+\sqrt{25+10*\sqrt{5}}}{4} · a^2\;\;\;\;≈ 8.8854·a^2\)

Height

\(\displaystyle h=\left(1+\frac{5-\sqrt{5}}{10}\right) · a\;\;\;\;≈1.5257 ·a \)