# Oblique Prism: Definition & Volume

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• 0:07 Introduction to Oblique Prisms
• 0:26 Definition of an Oblique Prism
• 1:21 Volume of an Oblique Prism
• 2:43 One More Example
• 3:19 Lesson Summary
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Lesson Transcript
Instructor: Mark Boster
There are many different shapes out there, one of which is a rectangular prism. But if it starts to tilt, then it is considered an oblique prism, and finding the volume can be tricky.

## Introduction to Oblique Prisms

Betsy asked her mother if she could take five cookies from the cookie jar. Her mother told her it was okay. Betsy stacked them one on top of the other. She didn't stack them exactly straight, but sort of slanted. If she had continued building, they would have toppled over, so she ate them!

## Definition of an Oblique Prism

Oblique is a strange word that means slant and comes from Latin. Therefore, if something is leaning, like a cookie tower, it's oblique. In math, oblique also means slanted, and applies to prisms. An oblique prism is a prism in which the bases are parallel, but one is not directly over the other, and all lateral faces are parallelograms. Lateral refers to the side of the prism.

However, not all oblique prisms are rectangular. You can have an oblique pentagonal prism (an oblique prism with five lateral faces), an oblique octagonal prism (an oblique prism with eight lateral sides), or even an oblique heptagonal prism (an oblique prism with seven lateral faces). This is important to know if you'd ever like to find the volume of an oblique prism.

## Volume of an Oblique Prism

To find the volume of an oblique prism, all you need to know is the area of the base and the height. To find the area of the base, you need to be tricky and know the formulas for finding the area of different shapes. For example, the area of a rectangle is length times width; for a triangle, it's 1/2 base times height. There are other formulas to find the area of the base for other shapes, too.

Because this is an oblique rectangular prism, you would find the area of the base by multiplying the length times the width of the base. Perhaps the base is 4 inches long and 8 inches wide. Therefore, the base area is 32 square inches.

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