Lesson 02: Finding Area by Decomposing and Rearranging | Unit 1: Area and Surface Area

Draw

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

Open Ended

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

Multiple Choice

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 to make the new figure shown. How does the area of the new figure compare with that of the original square?

• The area of the new figure is greater.

• The two figures have the same area.

• The area of the original square is greater.

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

Multiple Select

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 1/2 square units? Select all that apply.

• Figure A

• Figure B

• Figure C

• Figure D

Multiple Choice

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

• 5 meters
• 7 meters
• 8 meters
• 6 meters

Open Ended

A homeowner is deciding on one size of tiles to use to fully tile a rectangular wall in her bathroom that is 80 inches by 40 inches. The tiles are squares and come in three side lengths: 8 inches, 4 inches, and 2 inches. Tell whether or not you agree with the statement: Regardless of the size she chooses, she will need the same number of tiles. Explain your reasoning.

Open Ended

A homeowner is deciding on one size of tiles to use to fully tile a rectangular wall in her bathroom that is 80 inches by 40 inches. The tiles are squares and come in three side lengths: 8 inches, 4 inches, and 2 inches. Tell whether or not you agree with the statement: Regardless of the size she chooses, the area of the wall that is being tiled is the same. Explain your reasoning.

Open Ended

A homeowner is deciding on one size of tiles to use to fully tile a rectangular wall in her bathroom that is 80 inches by 40 inches. The tiles are squares and come in three side lengths: 8 inches, 4 inches, and 2 inches. Tell whether or not you agree with the statement: She will need two 2-inch tiles to cover the same area as one 4-inch tile. Explain your reasoning.

Open Ended

A homeowner is deciding on one size of tiles to use to fully tile a rectangular wall in her bathroom that is 80 inches by 40 inches. The tiles are squares and come in three side lengths: 8 inches, 4 inches, and 2 inches. Tell whether or not you agree with the statement: She will need four 4-inch tiles to cover the same area as one 8-inch tile. Explain your reasoning.

Open Ended

A homeowner is deciding on one size of tiles to use to fully tile a rectangular wall in her bathroom that is 80 inches by 40 inches. The tiles are squares and come in three side lengths: 8 inches, 4 inches, and 2 inches. Tell whether or not you agree with the statement: If she chooses the 8-inch tiles, she will need a quarter as many tiles as she would with 2-inch tiles. Explain your reasoning.