# Lesson 15

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 heart-shaped boxes or house-shaped 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.

### Student Facing

• I can calculate the the volume of a prism with a complicated base by decomposing the base into quadrilaterals or triangles.