Unit 1 Lesson 2

GRADE 6 UNIT 1 LESSON 2
Finding Area by Decomposing and
Rearranging

Learning Goal

Let’s create shapes and find their areas.

Learning Targets

• I can explain how to find the area of a figure that is composed of other shapes.

• I know how to find the area of a figure by decomposing it and rearranging the parts.

• I know what it means for two figures to have the same area.

Lesson Terms

area

compose

decompose

region

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WARM UP
What Is Area?

You may recall that the term area tells us something about the number of squares inside a
two-dimensional shape.

a. Here are four drawings that each show squares inside a shape. Select all drawings

whose squares could be used to find the area of the shape. Be prepared to explain
your reasoning.

b. Write a definition of area that includes all the information that you think is important.

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ACTIVITY 1
Composing Shapes

Your teacher will give you one square and some small, medium, and large right triangles.
The area of the square is 1 square unit.

a. Notice that you can put together two small triangles to make a square. What is the

area of the square composed of two small triangles? Be prepared to explain your
reasoning.

b. Use your shapes to create a new shape with an area of 1 square unit that is not a

square. Trace your shape.

Digital version

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c. Use your shapes to create a new shape with an area of 2 square units. Trace your

shape.

d. Use your shapes to create a different shape with an area of 2 square units. Trace your

shape.

e. Use your shapes to create a new shape with an area of 4 square units. Trace your

shape.

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Are you ready for more?

Find a way to use all of your pieces to compose a single large square. What is the area of
this large square?

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ACTIVITY 2
Tangram Triangles

Recall that the area of the square you saw earlier is 1 square unit. Complete each
statement and explain your reasoning.

a. The area of the small triangle is

square units. I know this because

b. The area of the medium triangle is

square units. I know this because

c. The area of the large triangle is

square units. I know this because

Lesson 2 Summary

Here are two important principles for finding area:

1. If two figures can be placed one on top of the other so that they match up exactly,

then they have the same area.

2. We can decompose a figure (break a figure into pieces) and rearrange the pieces

(move the pieces around) to find its area.

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Here are illustrations of the two
principles.

• Each square on the left can be decomposed into 2 triangles. These triangles can be

rearranged into a large triangle. So the large triangle has the same area as the 2
squares.

• Similarly, the large triangle on the right can be decomposed into 4 equal triangles. The

triangles can be rearranged to form 2 squares. If each square has an area of 1 square
unit, then the area of the large triangle is 2 square units. We also can say that each
small triangle has an area of

square unit.

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