Lesson 3

Reasoning to Find Area

Let’s decompose and rearrange shapes to find their areas.

Problem 1

Find the area of each shaded region. Show your reasoning.

3 figures on a grid labeled A, B, C.

 

Problem 2

Find the area of each shaded region. Show or explain your reasoning.

4 figures labeled A, B, C, D.

Problem 3

Two plots of land have very different shapes. Noah said that both plots of land have the same area.

Two shapes labeled “plot A” and “plot B”.

Do you agree with Noah? Explain your reasoning.

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.

  1. Regardless of the size she chooses, she will need the same number of tiles.
  2. Regardless of the size she chooses, the area of the wall that is being tiled is the same.
  3. She will need two 2-inch tiles to cover the same area as one 4-inch tile.
  4. She will need four 4-inch tiles to cover the same area as one 8-inch tile.
  5. If she chooses the 8-inch tiles, she will need a quarter as many tiles as she would with 2-inch tiles.
(From Unit 1, Lesson 2.)