How to Find the Height of a Rectangular Prism



How to Find the Height of a Rectangular Prism?

To be able to understand how to find the height of a rectangular prism, first let us see what exactly a rectangular prism is. To begin with, let us first understand what a prism is.

Prism:
A prism is not a plane figure. It is a solid three dimensional figure. An object such that all its cross sections in any one direction are same is called a prism. See pictures above:   
 
If the base of the prism is a triangle it is a triangular prism as shown in the first picture.
Similarly a prism with rectangular base is a rectangular prism. A special rectangular prism with square base is called a cube. 
A pentagonal prism has base of a pentagon and a hexagonal prism has base of a hexagon. All prisms have two bases of same shape and the sides faces are all rectangles. 

Rectangular Prism:

A rectangular prism has all rectangular faces. A rectangular prism has six faces, 8 vertices or corners and 12 edges. It is also called a cuboid. Any pair of opposite faces are same in size and dimensions. Any one such pair of opposite faces is termed as the two bases.   
 

Height of a Rectangular Prism:

The perpendicular distance between the bases is called the height of a rectangular prism. See picture above:  

 
Therefore we see that a rectangular prism primarily has three dimensions, the length and width of the base and the height. 
The length and width of base are collectively called the area of the base.

How to Calculate the Height:

The height of a rectangular prism could be calculated by using the following method and the formula given below.

If we know the area of the base and the volume of the prism then the height can be calculated using the formula:
H = Volume/Area of base.
Where, Area of base = length of base x width of base.
For example: Find the height of a rectangular prism with volume = 70 cm3 and length and width of base equal to 7 and 5 cm respectively.
Solution: Volume of prism = 70 cm3
Area of base = length of base x width of base
=>    Area of base = 7 * 5 = 35 cm2
=>    Height = h = volume/area of base = 70/35 = 2cm
=>    Therefore answer = 2 cm.