Volume of Parallelepiped Formula

What is a Parallelepiped?

To work with any parallelepiped formula, we need to know what precisely a parallelepiped is. A parallelepiped is a three-dimensional structure constructed by six parallelograms in symmetry. A parallelepiped is identified as three sets of four parallel edges with equally sized edges within each set.

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Geometric Figures Associated With Parallelepiped

The prism's base planes may very well be considered as any of the three pairs of parallel sides.

A cuboid is correlated to a rectangle in much the same fashion as a cube is closely similar to a square, and similarly, a parallelepiped is related to a parallelogram.

What Do You Need to Know to Find the Volume of a Parallelepiped?

To find the parallelepiped formula for the volume, we need to know the measures of two things:

  1. S which is the area of the bottom

  2. H which is the height of the parallelepiped

What is the Formula of Volume of a Parallelepiped?

The formula is:



V = the volume of the parallelepiped

Also, the formula for volume of parallelepiped = absolute value of the scalar triple product, i.e., a · (b × c)

What Is The Volume Of A Parallelepiped Formula In A Vector?

The volume of the parallelepiped spanned by a, b, and c is

Volume V=area of base⋅height=∥a×b∥ ∥c∥ |cosϕ|


Since the angle between c and a×b in the formula of volume of parallelepiped might potentially be greater than π/2 based on the order between a and b, we will have to use the absolute value in the volume of the parallelepiped formula vector.

Solved Example for Rectangular Parallelepiped Formula


The size of the parallelepiped is 9 ft. long, 6 ft. wide, and 12 ft. deep. Calculate the volume.


According to the formula of rectangular parallelepiped,

Volume V= Length × Width × Height (From equation (1) volume of parallelepiped formula)

Therefore, V= 9*12*6 =648ft³


Find the volume of parallelepiped where 40cm2 is the area of the bottom, and 30 cm is the height of the parallelepiped.


According to the volume of parallelepiped formula,


where S=40 cm2

H= 30cm

Therefore, V=40*30=120 cm³

FAQs (Frequently Asked Questions)

Q1. What is the Formula of Rectangular Parallelepiped?

Answer: When the six surfaces of a parallelepiped are rectangular, it is called a rectangular parallelepiped. It's a three-dimensional box framework.

All of the parallel edges here are of the equivalent length.

The rectangular parallelepiped volume formula is:

V= Surface Area × Height.... (1)

In this rectangular parallelepiped formula,

Surface area = the area of a rectangle, i.e.,

Surface area = Length × Width

Therefore, from equation (1),

V = Length × Width × Height

Hence, to calculate the volume, we need to know the measures of the:

  1. Length

  2. Width

  3. Height

Q2. What is the Area of the Parallelepiped Formula?

Answer: Area of parallelepiped A = Length × Height

For the Lateral Surface Area (LSA) of a parallelepiped, the formula is:

LSA = Perimeter of the base × Height

For the Total Surface Area (TSA) of a parallelepiped, the formula is:

TSA = LSA + 2*Base Area

= (Perimeter of the base × Height) + 2*Base Area