Lesson 12

More Nets, More Surface Area

Let’s draw nets and find the surface area of polyhedra.

Problem 1

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

Triangular prism, dimensions and areas of faces provided.
  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

Twelve cubes are stacked to make this figure.

Steps, bottom row 3 cubes, middle row 2 cubes, top row 1 cube
  1. What is its surface area?
  2. How would the surface area change if the top two cubes are removed?
(From Unit 1, Lesson 10.)

Problem 4

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

Two polyhedra labeled A and B. Polyhedron A has sides labeled 5, 4, and 10. Polyhedron B has sides labeled 4, 10, 13, 13, and 13.
Figure A net of rectangular prism. Figure B rectangular pyramid.

Problem 5

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

    Net of a square pyramid. Base 4 by 4. Height of triangular faces = 5.
  2. What is the surface area of the figure? (One grid square is 1 square unit.)
(From Unit 1, Lesson 11.)