In grade 6, students used nets made up of rectangles and triangles to find the surface area of three-dimensional figures. In this lesson they find surface areas of prisms, and see that structure of a prism allows for shortcuts in adding up the areas of the faces. They see that if the prism is sitting on its base, then the vertical sides can be unfolded into a single rectangle whose height is the height of the prism and whose length is the perimeter of the base. The purpose of the lesson is not to come up with a formula for the surface area of a prism, but to help students see and make use of the structure of the prism to find surface area efficiently (MP7).
- Calculate the surface area of a prism, and explain (in writing) the solution method.
- Comprehend that surface area and volume are two different attributes of three-dimensional objects and are measured in different units.
- Interpret different methods for calculating the surface area of a prism, and evaluate (orally and in writing) their usefulness.
Let’s look at the surface area of prisms.
Assemble the net from the blackline master to make a prism with a base in the shape of a plus sign. Make sure to print the blackline master at 100% scale so the dimensions are accurate. This prism will be used for both the warm-up and the following activity.
- 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.
base (of a prism or pyramid)
The word base can also refer to a face of a polyhedron.
A prism has two identical bases that are parallel. A pyramid has one base.
A prism or pyramid is named for the shape of its base.
A cross section is the new face you see when you slice through a three-dimensional figure.
For example, if you slice a rectangular pyramid parallel to the base, you get a smaller rectangle as the cross section.
A prism is a type of polyhedron that has two bases that are identical copies of each other. The bases are connected by rectangles or parallelograms.
Here are some drawings of prisms.
A pyramid is a type of polyhedron that has one base. All the other faces are triangles, and they all meet at a single vertex.
Here are some drawings of pyramids.
The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps.
For example, if the faces of a cube each have an area of 9 cm2, then the surface area of the cube is \(6 \boldcdot 9\), or 54 cm2.
Volume is the number of cubic units that fill a three-dimensional region, without any gaps or overlaps.
For example, the volume of this rectangular prism is 60 units3, because it is composed of 3 layers that are each 20 units3.