Lesson 8: Area of Triangles
About this lesson
This lesson builds on students’ earlier work decomposing and rearranging regions to find area. It leads students to see that, in addition to using areareasoning methods from previous lessons, they can use what they know to be true about parallelograms (i.e. that the area of a parallelogram is \(b⋅h\)) to reason about the area of triangles.
Students begin to see that the area of a triangle is half of the area of the parallelogram of the same height, or that it is the same as the area of a parallelogram that is half its height. They build this intuition in several ways:
 by recalling that two copies of a triangle can be composed into a parallelogram;
 by recognizing that a triangle can be recomposed into a parallelogram that is half the triangle’s height; or
 by reasoning indirectly, using one or more rectangles with the same height as the triangle.
They apply this insight to find the area of triangles both on and off the grid.
Lesson overview
 8.1 Warmup: Composing Parallelograms (10 minutes)
 8.2 Activity: More Triangles (25 minutes)

8.3 Optional Activity: Decomposing a Parallelogram (25 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 8.4 Cooldown: An Area of 14 (5 minutes)
Learning goals:
 Draw a diagram to show that the area of a triangle is half the area of an associated parallelogram.
 Explain (orally and in writing) strategies for using the base and height of an associated parallelogram to determine the area of a triangle.
Learning goals (student facing):
 Let’s use what we know about parallelograms to find the area of triangles.
Learning targets (student facing):
 I can use what I know about parallelograms to reason about the area of triangles.
Required materials:
 tape
 preprinted slips, cut from copies of the blackline master
 glue or gluesticks
 geometry toolkits
Required preparation:
 Students need access to tape or glue; it is not necessary to have both.
 Each copy of the blackline master contains two copies of each of parallelograms A, B, C, and D.
 Prepare enough copies so that each student receives two copies of a parallelogram.
Glossary:
 Access the complete Grade 6 glossary.
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses.