Lesson 3: Practice Problems

Problem 1

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

  1. An irregular blue shape on a blank grid with a height of 5 on the left and a width of 7 on the bottom. The rest of the shape stair steps down from the top left to bottom right.
  2. A blue square 6x6 on a blank grid with two squares cut out, each measuring 2x2.
  3. A blue shape made up of a 2x6 rectangle and a triangle with a base of 6 and height of 2. The shape looks like a house.

Problem 2

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

  1. A blue L shaped figure with sides of 6 cm, 6 cm, 2 cm, and 2 cm.
  2. A blue rectangle with sides of 8 cm and 5 cm. There is a white 2x3 rectangle cutout sitting diagonally in the middle.
  3. A blue rectangle with sides 10 cm x 15 cm. There is a white rectangle cutout in the middle with side 9x6.
  4. A blue isosceles triangle with a height of 5 cm and base of 16 cm divided into two 8 cm segments

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”. Plot “A“is a rectangle and plot “B” is the same height, but has a triangular shape removed from the right side, and an identical triangle shape added to the left side.

Do you agree with Noah? Explain your reasoning.

Problem 4 From Unit 1 Lesson 2

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.