Volume and surface area of the prism

The measurement formulas for the prism simplify in the case of a right prism and in that of the rectangular parallelepiped.

Property — Formulas of the prism

• Volume: $V = S_b\cdot h$, that is, the area of the base times the height (the distance between the two planes of the bases).
• Lateral surface area: the sum of the areas of the lateral faces. For a right prism it equals $S_{\text{lat}} = p_b\cdot h$ (perimeter of the base times the height).
• Rectangular parallelepiped with dimensions $a\times b\times c$: $V = abc, \qquad S_{\text{tot}}=2(ab+bc+ca), \qquad d = \sqrt{a^2+b^2+c^2}.$
• Volume of the parallelepiped using the scalar triple product: if the three edges are the vectors $\vec u,\vec v,\vec w$, then $V = |\vec u\cdot(\vec v\times\vec w)|$.

Links

Topics: Synthetic geometry of space
Concepts: Parallelepiped · Prism · Surface area · Volume
Skills: Using formulas