Lesson 13
Decomposing Bases for Area
Lesson Narrative
In this lesson, students continue working with the volume of right prisms. They encounter prisms where the base is composed of triangles and rectangles, and decompose the base to calculate the area. They also work with shapes such as heartshaped boxes or houseshaped figures where they have to identify the base in order to see the shape as a prism and calculate its volume (MP1). When students look for the prism structure in a shape to solve a problem, they are engaging in MP7.
Learning Goals
Teacher Facing
 Critique (orally) different methods for decomposing and calculating the area of a prism’s base.
 Explain (orally and in writing) how to decompose and calculate the area of a prism’s base, and then use it to calculate the prism’s volume.
Student Facing
Let’s look at how some people use volume.
Learning Targets
Student Facing
 I can calculate the the volume of a prism with a complicated base by decomposing the base into quadrilaterals or triangles.
Glossary Entries

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.

cross section
A cross section is the new face you see when you slice through a threedimensional figure.
For example, if you slice a rectangular pyramid parallel to the base, you get a smaller rectangle as the cross section.

prism
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.

pyramid
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.

volume
Volume is the number of cubic units that fill a threedimensional region, without any gaps or overlaps.
For example, the volume of this rectangular prism is 60 units^{3}, because it is composed of 3 layers that are each 20 units^{3}.