Unit 1, Lesson 9
Formula for the Area of a Triangle
Grade 6
Preparation
Lesson Narrative
In this lesson, students begin to reason about areas 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 see that any side of a triangle can be its base, as is the case for parallelograms. They also learn that the height that corresponds to a chosen base is the length of a perpendicular segment that connects the base to the opposite vertex.
Next, they identify base-height measurements of triangles and use them to determine area. Then students look for a pattern in their reasoning to help them write a formula for finding the area of any triangle (MP8). They also have a chance to build an informal argument about why the formula works for any triangle (MP3).
- 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.
Let’s write and use a formula to find the area of a triangle.
Required Materials
Activity 2
Required Preparation
None
For each side of a triangle, there is 1 vertex that is not on that side. This is the opposite vertex.
Point is the opposite vertex to side .