Hexagonal Prism: Properties, Formula & Examples

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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

In this lesson, we will learn what a hexagonal prism is and what it looks like. You'll also become familiar with the surface area and volume formulas for this 3-dimensional shape. When you're done, you can even test your knowledge with a quiz!

Hexagonal Prism

A hexagon is a 6-sided polygon. A prism is a 3-dimensional object that has two parallel ends, called bases, that have the same size and shape. The sides of a prism, called faces, are parallelograms. Based on these definitions, it's probably easy for you to figure out that a hexagonal prism is a prism with two bases that are hexagons and six faces that are rectangles.

Hexagonal prisms can be regular or irregular. A regular hexagonal prism is a hexagonal prism with regular hexagons as bases. If you're imagining a hexagon right now, you're probably imagining a hexagon where all the sides are the same length. That's basically what the bases of the prism look like.

An irregular hexagonal prism is the opposite. It has hexagon bases that are irregular, so the sides of its hexagon bases don't have all the same length.

There are hexagonal prisms to be observed in the world around us. Some examples include a pencil (before it's sharpened, of course), a nut, or a stone, among many others.

Because hexagonal prisms show up everywhere, it can be useful for some of us to know how to calculate the surface area and volume of these objects.

Surface Area of a Hexagonal Prism

The surface area of a 3D object is the area of all of the object's surfaces added together. Therefore, the surface area of a hexagonal prism would be the area of both of its bases plus the area of all of its six faces. That is, Surface Area (SA) = 2 * (area of hexagon base) + area of face 1 + area of face 2 + area of face 3 + area of face 4 + area of face 5 + area of face 6. This is also the formula we would use if our hexagonal prism is irregular. Pretty straightforward, right?

When we're dealing with a regular hexagonal prism, we can simplify this formula. But before we do this, we need to know a few facts. First, notice that in a regular hexagonal prism, all of the rectangular faces have the same area. To find the area of one of these rectangles, we can multiply its length times its width. Its length is the height of the prism (called h), and the width is the length of one of the sides of the hexagon bases (call it s). Therefore, the area of one of the rectangle faces is sh, and all six of the faces have this same area.

Second, we notice that a regular hexagon has an apothem. An apothem is the line from the center of the hexagon to the center of one of the hexagon's sides.

When we know the length of a regular hexagon's apothem, a, and the length of one of its sides, s, we can find the area of the hexagon using the formula A = 3as.

Using these facts, we can simplify our surface area formula.

This simplification gives that the surface area of a regular hexagonal prism is SA = 6s(a + h), where s = side length of the base, a = apothem length, and h = height of the prism.

For example, suppose we wanted to know the surface area of a building that's shaped like a regular hexagonal prism that has a base side length of 40 feet, apothem length of 35 feet, and a height of 20 feet. To do this, we'd plug in s = 40, a = 35, and h = 20 into our formula to get SA = 6 * 40 * (35 + 20) = 240(55) = 13,200 square feet.

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