Elongated Triangular Pyramid Calculation

The elongated triangular pyramid has an equilateral triangle as its base. The sides of the elongated pyramid are bounded by 3 equilateral triangles and 3 squares. All edges have the same length. The elongated triangular pyramid is one of the Johnson solids (J₇)

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 Triangular Pyramids

Volume

\(\displaystyle V= \left(\frac{\sqrt{2}+3·\sqrt{3}}{12}\right)·a^3\) \(\displaystyle \;\;\;\;≈ 0.5509 ·a^3\)

Surface area

\(\displaystyle S= (3+\sqrt{3})· a^2\;\;\;\;≈ 4.732 ·a^2\)

Height

\(\displaystyle h=\left(1+\frac{\sqrt{6}}{3}\right) · a\;\;\;\;≈1.8165 ·a \)