Lesson 3
Reasoning to Find Area
Problem 1
Find the area of each shaded region. Show your reasoning.
Solution
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Problem 2
Find the area of each shaded region. Show or explain your reasoning.
Solution
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Problem 3
Two plots of land have very different shapes. Noah said that both plots of land have the same area.
Do you agree with Noah? Explain your reasoning.
Solution
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Problem 4
A homeowner is deciding on the 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. State if you agree with each statement about the tiles. Explain your reasoning.
- Regardless of the size she chooses, she will need the same number of tiles.
- Regardless of the size she chooses, the area of the wall that is being tiled is the same.
- She will need two 2-inch tiles to cover the same area as one 4-inch tile.
- She will need four 4-inch tiles to cover the same area as one 8-inch tile.
- If she chooses the 8-inch tiles, she will need a quarter as many tiles as she would with 2-inch tiles.
Solution
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(From Unit 1, Lesson 2.)