# Lesson 9

Formula for the Area of a Triangle

### Lesson Narrative

In this lesson students begin to reason about area of triangles more methodically: by generalizing their observations up to this point and expressing the area of a triangle in terms of its base and height.

Students first learn about bases and heights in a triangle by studying examples and counterexamples. They then identify base-height measurements of triangles, use them to determine area, and look for a pattern in their reasoning to help them write a general formula for finding area (MP8). Students also have a chance to build an informal argument about why the formula works for any triangle (MP3).

### Learning Goals

Teacher Facing

• Compare, contrast, and critique (orally) different strategies for determining the area of a triangle.
• Generalize a process for finding the area of a triangle, and justify (orally and in writing) why this can be abstracted as $\frac12 \boldcdot b \boldcdot h$.
• Recognize that any side of a triangle can be considered its base, choose a side to use as the base when calculating the area of a triangle, and identify the corresponding height.

### Student Facing

Let’s write and use a formula to find the area of a triangle.

### Student Facing

• I can use the area formula to find the area of any triangle.
• I can write and explain the formula for the area of a triangle.
• I know what the terms “base” and “height” refer to in a triangle.

Building Towards

### Glossary Entries

• opposite vertex

For each side of a triangle, there is one vertex that is not on that side. This is the opposite vertex.

For example, point $$A$$ is the opposite vertex to side $$BC$$.