Lesson 12: Practice Problems

Problem 1

Jada drew a net for a polyhedron and calculated its surface area.

A net made up of a 4x5 rectangle, 4x4 square, and a 3x4 rectangle. There are right triangles attached to the square with a base of 3, a height of 4, and a diagonal of 5.

  1. What polyhedron can be assembled from this net?

  2. Jada made some mistakes in her area calculation. What were the mistakes?

  3. Find the surface area of the polyhedron. Show your reasoning.

Problem 2

A cereal box is 8 inches by 2 inches by 12 inches. What is its surface area? Show your reasoning. If you get stuck, consider drawing a sketch of the box or its net and labeling the edges with their measurements.

Problem 3 From Unit 1 Lesson 10

Twelve cubes are stacked to make this figure.

12 cubes stacked to make 3 stairs with heights of 1, 2, and 3 and rows of 2 cubes.

  1. What is its surface area?

  2. How would the surface area change if the top two cubes are removed?

Problem 4

Here are two polyhedra and their nets. Label all edges in the net with the correct lengths.

  1. Polyhedron with has sides labeled 5, 4, and 10
    A net of the previous shape.
  2. Polyhedron B with sides labeled 4, 10, 13, 13, and 13.
    A net of the previous shape.

Problem 5

A net on a grid made up of 4 equivalent triangles pointed up, down, left, right and connected to a square in the middle.

  1. What three-dimensional figure can be assembled from the net?

  2. What is the surface area of the figure? (One grid square is 1 square unit.)