Geometry

Lesson 4

Math

Unit 7

6th Grade

Lesson 4 of 17

Objective


Find the area of any triangle using height and base.

Common Core Standards


Core Standards

  • 6.G.A.1 — Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Criteria for Success


  1. Understand that the formula $${A={1\over2}bh}$$ can be used to find the area of any triangle.
  2. Understand that triangles with the same base and height will have the same area, regardless of the measures of the angles. 
  3. Identify the base and height in any triangle.
  4. Find the area of any triangle using base and height.

Tips for Teachers


  • This is the third of three lessons on finding the area of triangles. In this lesson, students develop the understanding through repeated reasoning that, regardless of the angles in a triangle, if the base and height are the same, then the area of the triangle is the same (MP.8).
  • Students continue to re-engage in 6.EE.2, evaluating the area of triangles using the formula.

Lesson Materials

  • Optional: Geoboards (1 per student)
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Anchor Problems


Problem 1

Four triangles were made on a geoboard. The pegs on a geoboard are equally spaced in the square grid.

 

Which triangle has the greatest area? The least area? Do any of the triangles have the same area? Why is that the case? 

Guiding Questions

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References

Illustrative Mathematics Same Base and Height, Variation 1

Same Base and Height, Variation 1, accessed on March 16, 2018, 3:42 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

For each triangle, circle a base measurement that you can use to find the area of the triangle. Then, find the area of any three triangles.

a.   

b.   

c.   

d.   

e.   

Guiding Questions

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References

Open Up Resources Grade 6 Unit 1 Lesson 99.3 Applying the Formula for Area of Triangles

Grade 6 Unit 1 Lesson 9 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 16, 2018, 3:44 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Find the area of the triangle.

Guiding Questions

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Problem Set

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Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


Use the triangles below to answer the following.

a.   Which of the triangles has the largest area?

  1. a.    $${{\triangle ABC}}$$

  2. b.    $${\triangle ABD}$$

  3. c.    $${\triangle ABE}$$

  4. d.    $${\triangle ABF}$$

  5. e.   They all have the same area.

  6. f.   There is not enough information to answer.

b.    Draw another triangle that has the same area of $${{\triangle ABC}}$$ in the grid below and explain why it has the same area of $${{\triangle ABC}}$$.

Student Response

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References

Illustrative Mathematics Same Base and Height, Variation 2

Same Base and Height, Variation 2, accessed on March 16, 2018, 3:49 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems that have decimal measurements to provide opportunities for fluency practice.
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Lesson 3

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Lesson 5

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Area of Triangles, Quadrilaterals, and Polygons

Topic B: Polygons in the Coordinate Plane

Topic C: Volume of Rectangular Prisms

Topic D: Nets and Surface Area

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