Area of a Triangle Lesson Plan

Introduction

Start the lesson by asking students what they already know about area. This can help them recall prior knowledge that will help them in the exploratory activity.

You can give students some time to think about their responses before sharing their answers. Encourage students to include anything they know about any of the shapes they are familiar with if they are unsure where to start. 

Exploratory activity

For the exploratory activity, students should work in groups of 2-4 to work on the activity, but each student should get their own copy of the Exploratory Activity Student Sheet to write their thoughts and ideas.

To facilitate this activity, your goal is to allow students to freely discuss their ideas with their groups. Allow students at least `10` minutes to process their thinking and determine if their strategy will work. If students are struggling, you may consider telling them to “think outside the box” so they think beyond just the triangle. Allow students to start with the first `3` triangles.

Recognizing the relationship between triangles and parallelograms/rectangles

Students will eventually recognize that a copy of the triangle they are given helps them form a parallelogram (or rectangle). For students that recognize the relationship with parallelograms, they will likely already have an understanding of identifying the base and height of the triangle. For students who recognize the relationship with rectangles, it may be helpful to remind them that rectangles are parallelograms. This can help simplify identifying the base and height for these students.

Relating triangles and parallelograms

Display slide 2 and have students look at the triangle and the parallelogram. You can have them think about how the shapes are related, then how their areas are related.

Students should first be able to recognize that the shaded triangle is half of the parallelogram. 

Since they know that they can find the area of a parallelogram by multiplying the base by the height, you can first have them find the area of the parallelogram. Then students will recognize to find the area of the triangle, they just need to divide that answer by `2`. 

Formalizing the formula for area of a triangle

Congratulate students on discovering a way to find the area of a triangle. Let students know that we will be writing a formula that we can apply to find the area of any triangle. Remind students that, just like with parallelograms, the base and the height of a triangle are perpendicular. Work with students to recognize that since they found the area of the parallelogram by multiplying the base by the height, that will be the first part of the formula. Write out `b \times  h`. Next, they divided by `2`. Show the formula written as `\frac{b \times h}{2}`. 

Explain to students that dividing by `2` is the same as multiplying by `1/2` so students might see the formula written as `1/2 \times b\times h`. Emphasize that these are the same formula. 

Applying the formula

Students should apply their formula to the second set of triangles. Allow students to work with a partner or table group. With this set of triangles, encourage students to identify the base and height of each triangle and label the base and height of the triangle. Although students should have discussed it, make sure students can explain how they identified the base and height for each triangle.

Verbal description example

It may be beneficial for students also to practice finding the area of a triangle from a description. For some students, not having the image may cause some struggles. Encourage them to make a drawing of the triangle and label the base and height.