~ 7.14 ~

Surface Area of Right Prisms

<< Previous

Unit 7

Next >>

Learning Targets

I can find and use shortcuts when calculating the surface area of a prism.
I can picture the net of a prism to help me calculate its surface area.

Notes

To find the surface area of a three-dimensional figure whose faces are made up of polygons, we can find the area of each face, and add them up!

Sometimes there are ways to simplify our work. For example, all of the faces of a cube with side length s are the same. We can find the area of one face, and multiply by 6. Since the area of one face of a cube is s², the surface area of a cube is 6s².

We can use this technique to make it faster to find the surface area of any figure that has faces that are the same.

For prisms, there is another way. We can treat the prism as having three parts: two identical bases, and one long rectangle that has been taped along the edges of the bases. The rectangle has the same height as the prism, and its width is the perimeter of the base. To find the surface area, add the area of this rectangle to the areas of the two bases.

Cube (a special type of rectangular prism)

Rectangular Prism

Triangular Prism

Surface area review (article) | Surface area | Khan AcademyReview surface area and try some practice problems.

Activities

14.2 So Many Faces

Here is a picture of your teacher's prism. It is multifaceted (having many aspects of sides).

Three students are trying to calculate the surface area of this prism.

Noah says, “This is going to be a lot of work. We have to find the areas of 14 different faces and add them up.”
Elena says, “It’s not so bad. All 12 rectangles are identical copies, so we can find the area for one of them, multiply that by 12 and then add on the areas of the 2 bases.”
Andre says, “Wait, I see another way! Imagine unfolding the prism into a net. We can use 1 large rectangle instead of 12 smaller ones.”

Do you agree with any of them? Explain your reasoning.
How big is the “1 large rectangle” Andre is talking about? Explain or show your reasoning. If you get stuck, consider drawing a net for the prism.
Will Noah’s method always work for finding the surface area of any prism? Elena’s method? Andre’s method? Be prepared to explain your reasoning.
Which method do you prefer? Why?

Add to Your Notes

Prisms can always be cut into three pieces:

2 bases
one rectangle whose length is the perimeter of a base and whose width is the height of the prism

14.3 Revisiting a Pentagonal Prism

Here are two methods to find the surface area of the prism. Choose one!
Use your chosen method to calculate the surface area of the prism. Show your thinking. Organize it so it can be followed by others.

Add to Your Notes

What is surface area?

The total area of all the exposed faces of an object.

What are some methods for calculating surface area of prisms?

Find the area of each face and total.
Find the area of the bases and add that to the area of the “big rectangle”.

Page updated

Report abuse