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What is a Triangular Prism? - Definition, Formula & Examples

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  • 0:05 Definition of a…
  • 0:50 The Different Parts of…
  • 2:06 Finding Surface Area
  • 3:49 Finding Volume
  • 4:58 Lesson Summary
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Lesson Transcript
Instructor: David Karsner
Triangular prisms are three-dimensional solids formed by putting rectangles and triangles together. In this lesson, learn how to find the size inside (volume) and outside (surface area) of a triangular prism.

Definition of Triangular Prism

Picture a box sitting on the floor. In math language, a common everyday box is a prism. A prism is a three-dimensional solid shape with two identical ends connected by equal parallel lines. Most boxes have rectangles or squares for their tops and bottoms. Let's imagine once again your box no longer has a rectangle for its top and bottom but triangles for both. This new box is called a triangular prism, or a prism with a triangle on either side. This lesson is concerned with what the parts of the triangular prism are called, and how to name them. The lesson will also show how to find the surface area (the amount of space on the outside) and the volume (the amount of space on the inside).

A triangular prism
prism triangle

The Different Parts of a Triangular Prism

If you cut your triangular prism apart and lay it flat on the table, you have created the net for your triangular prism, as shown in the image below.

A net for a triangular prism
net

Notice how your three dimensional triangular prism is made up two dimensional shapes, like rectangles and triangles. There are three rectangles and two triangles.

The two-dimensional shapes that form a three-dimensional shape are called faces. The top and bottom, which are triangles, are bases. The three rectangles are called lateral faces. A triangular prism has five faces consisting of two triangular bases and three rectangular lateral faces, and a base is also a face.

The parts of a triangular prism
Lateral faces in blue,  Bases in green

When two of the faces meet, they form a line segment called an edge. When three edges meet, they form a point, which is called a vertex (the plural of vertex is vertices). A triangular prism has 5 faces, 9 edges, and 6 vertices.

Triangular prism with vertices labelled
prism

When referring to parts of a prism, use the letters that have been assigned to each vertex. One of the bases is the triangle AFE, one of the edges is line segment BC, and one of the vertices is the point D.

Finding Surface Area

Surface area is the amount of space on the outside of an object. For example, if you were to wrap a box in wrapping paper, the amount of paper you would need is a question about surface area. To illustrate surface area of a triangular prism, let's go back to the net that was created earlier. You should have noticed that we had two triangles and three rectangles in the net, and these shapes formed the outside of the triangular prism.

To find the surface of the triangular prism, find the area of each of its pieces and then add them together. The surface area of triangular prism is the area of rectangles one, two, and three, and the area of triangles one and two. You can do this by using the formulas for area of rectangles and triangles or you could use this shortcut:

Step One: Find the perimeter of the triangle base, the p.

Step Two: Find the area of the triangle base, the A.

Step Three: Determine the height of the prism. the h.

Step Four: p x h + 2 * A = Surface Area

Let's look at an example:

Finding surface area
net

Step One: Perimeter = 5 + 8 + 5 inches = 18 inches

Step Two: Area of triangle base = (8 x 3)/2 = 12 square inches

Step Three: Height = 10 inches.

Step Four: 18 x 10 + 2(12) = 180+24 = 204 square inches

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