How To Find The Volume Of Parallelepiped

Volume of Parallelepiped

Parallelepiped Volume Formula

There are two formulas for finding volume of a parallelepiped. They are given as:
V = h·|a|·|b|·sin(γ)
Five = h·B
Where5 is the book,h is the elevation,a and b are the base of operations edge vectors, γ is the angle betwixt vectorsa andb, andB is the area of the base.

What is a Parallelepiped?

A parallelepiped is a three-dimensional shape made of six faces. It is the result of tilting the edges of a rectangular prism. Imagine pushing confronting the elevation corner of a box that is not perfectly rigid. The box volition camber in the direction that information technology is pushed. This forms a parallelepiped.

As we tin run into in the paradigm above, there are three pairs of congruent parallelograms on opposing sides of the figure. This is the virtually mutual style of parallelepiped. Nonetheless, non all parallelepiped shapes have three pairs of opposing congruent sides.

Information technology is easier to calculate the volume of parallelepiped type shapes if we understand that a parallelepiped is formed past six parallelograms. If we understand how to calculate book of a rectangular prism and tin visualize what a parallelepiped is, we need not memorize the formula. Finding the expanse of the base parallelogram and multiplying past the shape'due south height will give usa the volume.

Instance Problem

A given parallelepiped is made up of 3 pairs of congruent parallelograms. The base of operations parallelogram has an surface area of viii. The height of the parallelepiped is 4. What is its volume?
Solution:
one.) Since nosotros are given base expanse and height, we tin can utilize the simplified formula 5 = h∙B.
two.) Permit'due south plug the base surface area and pinnacle into the formula.
V = (4)(eight) = 32.
3.) The volume of the parallelepiped is 32.