Frustum of a Pyramid

Frustum of a Pyramid

Polyhedron obtained by cutting a pyramid with a plane that is parallel to its base and that meets all its generatrices. Of the two polyhedrons obtained, the polyhedron that does not contain the apex of the pyramid is called the frustum of the pyramid; the other is a pyramid.

By cutting a pyramid with a plane that is not parallel to its base, we obtain a truncated pyramid and a pyramid.

 ← Pyramid ← Truncated Pyramid

Formulas

Consider this frustum of a pyramid, where h = m $$\overline{\textrm{O}_{1}\textrm{O}_{2}}$$ :

• The total area A of the frustum of a right square pyramid with edge lengths a and b and height h, is given by the following formula: $$a^{2} + b^{2} + 2(a + b) × \sqrt{h^{2} + \dfrac{(a\space –\space b)^{2}}{4}}$$
• The volume V of the frustum of a right square pyramid with edge lengths a and b and a height h, is given by the following formula: V = $$\dfrac{h}{3}$$ × $$(a^{2} + \sqrt{a^{2} – b^{2}} + b^{2})$$
• The volume V of the frustum of a pyramid whose bases have an area of $$a^{2}$$ and $$b^{2}$$ and whose height is h, is given by the following formula: V = $$\dfrac{h}{3}$$ × $$(a^{2} + \sqrt{a^{2}b^{2}} + b^{2})$$