# Lesson 2

Finding Area by Decomposing and Rearranging

### Problem 1

The diagonal of a rectangle is shown.

1. Decompose the rectangle along the diagonal, and recompose the two pieces to make a different shape.

2. How does the area of this new shape compare to the area of the original rectangle? Explain how you know.

### Solution

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### Problem 2

Priya decomposed a square into 16 smaller, equal-size squares and then cut out 4 of the small squares and attached them around the outside of original square to make a new figure.

How does the area of her new figure compare with that of the original square?

A:

The area of the new figure is greater.

B:

The two figures have the same area.

C:

The area of the original square is greater.

D:

We don’t know because neither the side length nor the area of the original square is known.

### Solution

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### Problem 3

The area of the square is 1 square unit. Two small triangles can be put together to make a square or to make a medium triangle.

Which figure also has an area of $$1\frac 12$$ square units? Select all that apply.

A:

Figure A

B:

Figure B

C:

Figure C

D:

Figure D

### Solution

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### Problem 4

The area of a rectangular playground is 78 square meters. If the length of the playground is 13 meters, what is its width?

### Solution

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(From Unit 1, Lesson 1.)

### Problem 5

A student said, “We can’t find the area of the shaded region because the shape has many different measurements, instead of just a length and a width that we could multiply.”

Explain why the student’s statement about area is incorrect.

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 1.)