Calculate Regular Triangular Pyramid
Calculators and formulas to calculate a regular triangular pyramid
This function calculates various parameters of a regular triangular pyramid. The regular triangular pyramid has an equilateral triangle as its base and three isosceles triangles as lateral surface.
To calculate, enter the base length and the height. Then click on the 'Calculate' button.
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Formulas for the triangular pyramid
Edge length (\(\small{b}\))
\(\displaystyle b =\sqrt{h^2 + \frac{a^2}{3}}\)
Slant height (\(\small{s}\))
\(\displaystyle s = \sqrt{\frac{4 · b^2 - a^2}{4}} \)
Base area (\(\small{A}\))
\(\displaystyle A = \frac{\sqrt{3} · a^2}{4} \)
Slant area (\(\small{A_m}\))
\(\displaystyle A_m = \frac{ 3 · a·s}{2} \)
Surface (\(\small{S}\))
\(\displaystyle S = \frac{\sqrt{3} · a^2}{4} +\frac{ 3 · a·s}{2}\;\;= A+ A_m \)
Volume (\(\small{V}\))
\(\displaystyle V = \frac{\sqrt{3} · a^2 · h}{12} \)
Height (\(\small{h}\))
\(\displaystyle h = \frac{ 12· V}{ \sqrt{3} · a^2} \)
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