Pyramid
Definition, properties, and formulas for pyramid calculations
Definition and Properties
A pyramid is a polyhedron with a polygonal base and triangular side faces that meet at a single point, called the apex.
- A pyramid with an n-sided base has n+1 vertices, n+1 faces, and 2n edges
- The base is any polygon with at least three edges
- The side faces are triangles connecting base edges to the apex
- The center of gravity lies on the segment from base center to apex in a 1:3 ratio
The formulas below refer to a right square pyramid.
Formulas
Base side length a
\(\displaystyle a=\sqrt{\frac{P}{4}}\)
Radius to side center rₛ
\(\displaystyle r_s=\sqrt{\frac{A}{2}}\)
Radius to corner rᵥ
\(\displaystyle r_v=\sqrt{\left(\frac{a}{2}\right)^2+r_s^2}\)
Base perimeter P
\(\displaystyle P=4a\)
Base area A
\(\displaystyle A=a^2\)
Height h
\(\displaystyle h=\frac{3V}{A}=\sqrt{m^2-r_s^2}\)
Lateral height m
\(\displaystyle m=\sqrt{h^2+r_s^2}\)
Edge length k
\(\displaystyle k=\sqrt{m^2+\frac{a^2}{4}}\)
Area of one side M₁
\(\displaystyle M_1=\frac{ma}{2}\)
Lateral surface M
\(\displaystyle M=\frac{mP}{2}\)
Volume V
\(\displaystyle V=\frac{Ah}{3}\)
\(\displaystyle V=\frac{Ah}{3}\)
\(\displaystyle M=\frac{mP}{2}\)
\(\displaystyle h=\sqrt{m^2-r_s^2}\)
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