Elongated Pentagonal Pyramid
Calculators and formulas for an elongated pentagonal pyramid (Johnson solid J9)
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.
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Elongated Pentagonal Pyramid Formulas
Volume (\(\small{V}\))
\(\displaystyle V= \frac{5+\sqrt{5}+6·\sqrt{25+10·\sqrt{5}}}{24}·a^3\) \(\displaystyle \;\;\;\;≈ 2.022 ·a^3\)
Surface area (\(\small{S}\))
\(\displaystyle S= \frac{20+5·\sqrt{3}+\sqrt{25+10*\sqrt{5}}}{4} · a^2\;\;\;\;≈ 8.8854·a^2\)
Height (\(\small{h}\))
\(\displaystyle h=\left(1+\frac{5-\sqrt{5}}{10}\right) · a\;\;\;\;≈1.5257 ·a \)
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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