Lesson plan

In this lesson, students will learn how to find the area of a triangle. Through student discussion and discovery, students will understand the relationship between the area of a triangle, rectangle, and parallelogram. You can expect this lesson with additional practice to take one `45`-minute class period.

Grade 6

Geometry

6.G.A.1

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Students will be able to find the area of a triangle.

- Teacher slideshow
- Exploratory Activity Student Sheet
- Online Practice

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.

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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.

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.

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.

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`.

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.

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.

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.

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for finding the area of a triangle. Check out the online practice and assign to your students for classwork and/or homework!

Finding the Area of a Triangle Practice

Problem 1 of 5

<p>What is the area of the triangle? <br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal. </highlight></p><UiTriangleV2 data-props='{ "options": { "cell_size": 16, "rows": 14, "columns": 11, "padding": 1, "xOffset": 1, "yOffset": 0 }, "scale_factor": 8, "vertex": { "top": { "angle": 28 }, "left": { "angle": 97 }, "right": { "angle": 55 } }, "sides": { "base": { "label": { "label": "8 ft", "label_color": "black" }, "color": "black" }, "left": {}, "right": { "label": { "label": "17 ft" } }, "altitude": { "label": { "label": "14 ft", "label_color": "black" }, "color": "black" } }, "arcs": [ { "position": "altitude", "color": "black", "show_arc": true } ], "background_color": "white", "border_color": "black", "debug": false}'></UiTriangleV2>

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