What Is a Pentagonal Prism?

The Pentagon Building in Washington, D.C. is a regular, pentagonal prism.
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A pentagonal prism is a three-dimensional box whose bottom and top have five sides instead of the normal four. This means that the box also has five sides instead of the typical four. The Pentagon Building in Washington, D.C., is an example of a pentagonal prism.


A triangular prism had three sides.
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Prisms are three-dimensional boxes with two similar bases. The most recognizable prism has square or rectangular bases making it look like your typical box. A prism can have triangular bases giving it three sides, pentagonal bases giving it five sides, hexagonal bases giving it six sides, and so on.


The black patches on a soccer ball are pentagonal in shape.
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A pentagon is a five-sided polygon, just like a square is a four-sided polygon and a triangle is a three-sided polygon. If all five sides are equal or the same length, the figure is called a regular pentagon.


The most common calculation made on a pentagonal prism is to find its volume. To find the volume of any prism, you must multiply the area of the base of the prism by its height. To find the volume of a regular, pentagonal prism you need to know the apothem length (a), which is the measure from the center of the pentagon to the midpoint of any side, the length of any side (s), and the height (h) of the prism. You multiply (a)(s)(h)(5/2).

Surface Area

The surface area of a prism is expressed in square units, while the volume is expressed in cubic units.
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The second most common calculation made on a pentagonal prism is to find its surface area. To find the surface area of a pentagonal prism you need the same three numbers a, s, and h as you did for the volume. Multiply 5(a)(s) together and 5(s)(h) together and then add the two numbers.


About the Author

Lynn Wood is a professional writer who grew up on a dairy farm in rural Missouri. After completing her bachelor's degree in English and journalism at Brigham Young University-Idaho, she stayed there and taught in the university's math department for three years before settling down in Preston, Idaho. Wood now teaches high-school English.

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