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.

Required Materials

Learning Targets

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.

CCSS Standards

Addressing

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 \(BC\).

    triangle with points labeled A, B, C.