How to Find Surface Area and Volume of a Prism
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A prism is a three-dimensional figure, which means you can put things inside it. In other words, it has both volume and a surface area. The bases of a prism are always identical polygons. For example, if you have a square as one of the faces, you must have an identical square as the other face.
The Volume of a Prism
The volume is the amount of space inside a three-dimensional object. Here you’ll learn how to calculate the volume of prisms that have quadrilaterals as their faces.
Formula
The Volume of a Quadrilateral Prism
Example 1
You can calculate the volume of the quadrilateral prism above by multiplying the length, cm, by the width, cm, and the height, cm:
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Want to watch animated videos and solve interactive exercises about finding the surface area of prisms?
The Surface Area of a Prism
Now you’ll learn how to calculate the surface area of prisms. The surface area is the sum of all the areas from each face of a prism. So, you can simply calculate the area of each face, and add them all together in the end.
Formula
The surface area of a quadrilateral prism is
Example 2
You can see in this figure that there are three sets of faces, with each set having two faces that are equal to each other. That means that you only have to find the area of one face from each set, and multiply that answer by 2, to get both their areas. You then add the answers together to find the surface area, like this:
Example 3
A prism has a triangle with the area as its base, and height . Find the volume of the prism.
You find the volume by multiplying the base area with by height :
