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High School Trigonometry: Tutoring Solution30 chapters | 201 lessons

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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.

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).

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.

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.

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.

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.

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:

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

Volume is a three-dimensional measurement, and area is a two-dimensional measurement. Volume is the amount of space on the inside of an object. For example, if you were to fill your backyard pool with water for the summer season, the amount of gallons of water that you would need to fill it is a question about volume. Even though you have one more dimension to concern yourself with, the procedure for finding the volume of a triangular prism is similar to finding the surface area. To find the volume of a triangular prism, find the area of the triangular base and multiply by the height of the solid, like this:

Step One: Find the area of the triangular base, the *A*.

Step Two: Find the height of the prism, the *h*.

Step Three: *A* x *h* = the volume

Let's look at an example:

Step One: Area = (6 x 8)/2 = 24 square inches

Step Two: Height = 12 inches.

Step Three: 24 x 12 = 288 cubic inches, the volume

**Triangular prisms** are three-dimensional solids that have triangles for their bases and rectangles for their lateral faces. The line segment where two faces come together is an edge. The point that three edges come together is a vertex. The surface area is found by finding the perimeter of the triangle base and multiplying it by the height of the prism and adding the product of the base of the triangle with the height of the triangle. The volume is found by finding the area of the triangle and multiplying it by the height of the prism.

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High School Trigonometry: Tutoring Solution30 chapters | 201 lessons

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