Lesson 11

Polyhedra and Nets

Let's use nets to find the surface area of polyhedra.

Problem 1

Here are two three-dimensional figures.

Tell whether each of the following statements describes Figure A, Figure B, both, or neither.

Figure A triangular prism. Figure B triangular pyramid.
  1. This figure is a polyhedron.
  2. This figure has triangular faces.
  3. There are more vertices than edges in this figure.
  4. This figure has rectangular faces.
  5. This figure is a pyramid.
  6. There is exactly one face that can be the base for this figure.
  7. The base of this figure is a triangle.
  8. This figure has two identical and parallel faces that can be the base.

Problem 2

  1. Is this polyhedron a prism, a pyramid, or neither? Explain how you know.

    Prism with octagons as faces.

  2. How many faces, edges, and vertices does it have?

Problem 3

  1. What polyhedron can be assembled from this net? Explain how you know.

    net on a grid. 

  2. Find the surface area of this polyhedron. Show your reasoning.

Problem 4

  1. A parallelogram has a base of 12 meters and a height of 1.5 meters. What is its area?

  2. A triangle has a base of 16 inches and a height of \(\frac18\) inches. What is its area?
  3. A parallelogram has an area of 28 square feet and a height of 4 feet. What is its base?
  4. A triangle has an area of 32 square millimeters and a base of 8 millimeters. What is its height?
(From Unit 1, Lesson 8.)

Problem 5

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

Triangle shaded with a unshaded square located in the middle on the bottom.
(From Unit 1, Lesson 3.)