Regular Tetrahedron Formula
Pyramid on a triangular base is a tetrahedron. When a solid is bounded by four triangular faces then it is a tetrahedron. A right tetrahedron is so called when the base of a tetrahedron is an equilateral triangle and other triangular faces are isosceles triangles. When we encounter a tetrahedron that has all its four faces equilateral then it is regular tetrahedron.
Area of One Face of Regular Tetrahedron Formula:
\[\large A=\frac{1}{4}\sqrt{3}a^{2}\]
Total Surface Area of Regular Tetrahedron Formula:
\[\large A=a^{2}\sqrt{3}\]
Slant Height of a Regular Tetrahedron Formula:
\[\large a\left(\frac{\sqrt{3}}{2}\right)\]
Altitude of a Regular Tetrahedron Formula:
\[\large h=\frac{a\sqrt{6}}{3}\]
Volume of a Regular Tetrahedron Formula
\[\large V=\frac{a^{3}\sqrt{2}}{12}\]
Solved Example
Question:Â What is the volume of a tetrahedron with sides 10 cm ?
Solution:
Here,
a = 10 cm
Using the formula of Volume of a Regular Tetrahedron:
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