Student 1: Surface area is the number of square units that are needed to cover the surface of a three
Student 2: Surface area is just what you see of a three-dimensional object, not what is inside.
Mentor: Good, how do you find the surface area of a three dimensional object?
Student 1: Well, there are a lot of three dimensional objects such as cones, rectangular prisms and
triangular prisms. The formula for finding surface area cannot be the same for all of these
Mentor: That is true! Three-dimensional figures have different formulas for surface area depending on
their shape. Let's examine the surface area specifically of a triangular prism.
Mentor: Since we are finding the surface area of this shape, how many sides will we need to include?
Student 1: This is a triangular prism so it has 5 sides (the two triangular sides and three rectangular
sides). We have to make sure to count how many square units are on each of the five sides.
That will give us the entire area that covers the shape.
Mentor: Great! Lets first look at the top surface of this figure. How many square units cover this
Student 2: You are asking me to find the area. I remember learning that the area of a triangle is 1/2
times the base times the height.
Mentor: For this activity we are going to call the base of the trianglular prism the base width and
we are going to call the height of the prism the base depth.
Student 1: OK, then the base width is 4 units and the base depth is 6 units. Therefore, the area would
1/2 x 4 x 6 = 12 square units
Mentor: That is right. Now, are there any other surfaces on this triangular prism that would be
identical to the one we just worked with?
Student 1: The surface directly below this (the other triangular side of the prism) should have the same
amount of cubic units.
Mentor: That is true, but why?
Student 2: Well, the base width of the flat triangular shape will be the same (4 units) and the base
depth of the shape will be the same (6 units) so that means that the area should be the same
Mentor: Good. Now we have two of the surfaces covered (each 12 square units). Let's move to the side
of the shape facing towards the right. How many square units are on this surface?
Student 1: Well, one side looks like it is exactly 3 units, but I am not sure how many units are on the
other side of the shape. It looks slanted and I am not sure.
Mentor: Good observation. The side that is 3 units measures the prism height. The other length that
you are confused about is called the slant height. It can be hard to find the slant height on
triangular prisms. For this exercise I am going to go ahead and give you the slant height:
Student 2: OK, if the slant height is 6.32 units and the prism height is 3 units then the area of that
side would be 6.32 times 3, which equals 18.96 square units.
Mentor: Good. And is there another surface identical to this one on the triangular prism?
Student 2: Yes, the surface opposite of this one would be identical since it, too, would have a prism
height of 3 units and a slant height of 6.32 units.
Mentor: Excellent. Now we have four surfaces covered. Two of them are 12 square units each, and two
of them are 18.96 square units each. Lets take a look at the last side that we can see of this
three dimensional figure:
Student 1: This surface is easy! There are 4 units on one side and 3 units on the other.
Mentor: Right. The 4 units measure the base width and the 3 units measure the prism height. What will
you do to find the area of this shape?
Student 1: Since this is a rectangle all I have to do is multiply those two numbers. 4 (the base width)
times 3 (the prism height) gives me the area of the flat rectangle: 12 square units!
Student 2: Yes! And that means that we have found the area of five total sides. A triangular prism only
has five sides so we have all of the areas that we need now.
Mentor: Right! So we have:
two surfaces that are 12 square units
two surfaces that are 18.96 square units
one surface that is 12 square units.
Now, what is the total surface area of the triangular prism?
Student 1: To find the total surface area I would need to add all of the separate areas that I found
together. It would be:
12 = 73.92 square units!
Mentor: Great job! You just found the surface area of a triangular prism!