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How to Find Rectangular Prism Volume and Surface Area

rectangular prism volume: Two colorful blocks stacked on top of each other

How do you determine rectangular prism volume and surface area? Let's start by defining what this shape is.

A rectangular prism is a three-dimensional shape with two identical rectangular faces and one identical square face:

rectangular prism volume: Rectangular prism

Other examples of prisms include triangular prisms, square prisms, and polygon prisms:

rectangular prism volume: Examples of polygon prisms

Let's learn how to find the surface area and volume of a rectangular prism.

How to Find the Surface Area of a Rectangular Prism

Let's review the surface area of a rectangle.

The length, width, and height of a rectangular prism are made by six separate shapes that, when put together, creates a three-dimensional figure.

The surface area of a rectangle in prism form is the sum of the areas of all six shapes. Here is the formula for the surface area of a prism:

Formula for the surface area of a prism

Let's use this formula to find the surface area of the rectangular prism below:

Rectangular prism

Length: 12 feet

Width: 4 feet

Height: 4 feet

Formula for the surface area of a rectangular prism

If you need a refresher about the order of these calculations, remember the order of operations through the acronym PEMDAS (here’s how this works).

For surface area, always keep your answer in square units.

How to Find Rectangular Prism Volume

Now that we know how to find the surface area, let's move on to finding the volume of the rectangular prism. Volume is the amount of space that a three-dimensional figure takes up. For finding volume, use these formulas:

Formula to find the rectangular prism volume

The area of the base is the length times the width. So to get the final volume, you must multiply the height of the rectangular prism by the area of the base.

Let's use this formula to determine the volume of this prism, which must be expressed in cubic centimeters (cm³):

Rectangular prism

Length: 17 centimeters

Width: 7 centimeters

Height: 7 centimeters

Formula to find the rectangular prism volume

With volume, your answer should be in terms of units squared.

Rectangular Prism Volume and Surface Area

Once you understand that a rectangular prism includes some sets of identical shapes, it's much easier to find its surface area and volume.

The surface area of a rectangular prism is the sum of the areas of each side, and the volume of a rectangular prism is its length times width times height.

Knowing the surface area and volume formula for a rectangular prism makes it much easier to tackle other geometric shapes.

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