Understanding Rectangular Prisms: Help for Math Students

In middle school, you'll learn formulas for finding the surface area and volume of rectangular prisms. Keep reading for a complete introduction to this important geometry skill!

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Help with Rectangular Prisms

A rectangular prism is a solid, 3-dimensional object with three sets of parallel sides that are at right angles to one another. Bricks and packs of playing cards are rectangular prisms.

Surface Area

Surface area is the amount of 2-dimensional space that the surface of an object occupies. It's calculated by adding the areas of each of an object's surfaces. A rectangular prism has a total of six surfaces (sides), and they are all rectangular. You can find the area of a rectangle by multiplying its length and width (A = L x W).

To find the surface area of a rectangular prism, find the area of each of its sides and add them together. Or, since there are three pairs of identical sides, you can find the area of one of each of these sides. Then, multiply each area by two and add the results together. Here's an example of how to find surface area with a rectangular prism that's ten centimeters high, five centimeters wide and three centimeters long:

Surface area = 2LW + 2LH + 2HW

= 2(3)(5) + 2(3)(10) + 2(10)(5)

= 30 + 60 + 100

= 190 centimeters squared

Volume

The volume of a 3-dimensional object is found by multiplying the area of its base by its height (V = b x h). Since rectangular prisms always have rectangular bases, the area of the base is the product of its length and width (L x W). This, multiplied by the rectangular prism's height, produces the formula L x W x H. Here's an example of how to find the volume of a rectangular prism with a length of six inches, a width of nine inches and a height of two inches:

Volume = L x W x H

= 6 x 9 x 2

= 108 cubic inches

Units

Some geometry problems state the dimensions of objects in different types of units. For instance, you might be asked to find the volume of a rectangular prism with a length of one meter, a width of 15 centimeters and a height of 12 centimeters.

Since the length of one side is given in meters, while the lengths of the other two sides are given in centimeters, you'll need to convert the lengths so they're all in a single type of unit. In this case, it would be simplest to convert the length of one meter to 100 centimeters, and then solve the problem. Sometimes, problems will specify which unit you should report your answer in, which is a clue that the dimensions of the sides are not given in like units.

It's also important to give your answer in a unit appropriate to the type of measurement in the problem. Remember that line segments are measured using units like inches and centimeters, while areas are measured in square units, such as square inches and square centimeters. The volume of a solid is always given in cubic units, like cubic inches or cubic centimeters.

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