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Geometry for Kids6 chapters | 45 lessons

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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.

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!

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.

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.

To find the height of the oblique prism is a little tricky. Because it's obtuse, you need to measure from the top of the prism to the base. It won't be along the edge, but straight down. So, maybe the height is 5 inches. Therefore, we multiply 32 square inches by 5.

So now we have a problem that looks like this:

Base area = 32 sq in.

Height is 5 in.

Volume = B (32) x H (5). So the volume is 160 cubic inches.

Let's now look at one more example before calling it a day.

Because this is an oblique triangular prism, you need to find the area of the triangular base. This base has a 1-inch length and a 2-inch height. Remember that the formula for the area of a triangle is 1/2 base x height.

1 x 2 = 2

2 x 1/2 = 1 sq in.

Remember, volume = base area x height. This is what it looks like:

1 sq in. (base area) x 2 (height) = 2 cubic inches for the volume.

Oblique means slanted, so an **oblique prism** is a prism in which the bases are parallel, but not having one directly over the other, and all lateral faces are rectangular. Remember that **lateral** means the side. The formula for finding the volume of this type of prism is base area multiplied by the height. Finding the base area depends on the shape. For a rectangle, it's simply length times width. For a triangle, it's a little more complicated, with the formula being ½ base times height. Now you should be set for finding the volume for an oblique prism.

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Geometry for Kids6 chapters | 45 lessons

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