Lesson 11
Polyhedra and Nets
Problem 1
Here are two threedimensional figures.
Tell whether each of the following statements describes Figure A, Figure B, both, or neither.
 This figure is a polyhedron.
 This figure has triangular faces.
 There are more vertices than edges in this figure.
 This figure has rectangular faces.
 This figure is a pyramid.
 There is exactly one face that can be the base for this figure.
 The base of this figure is a triangle.
 This figure has two identical and parallel faces that can be the base.
Solution
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Problem 2

Is this polyhedron a prism, a pyramid, or neither? Explain how you know.
 How many faces, edges, and vertices does it have?
Solution
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Problem 3

What polyhedron can be assembled from this net? Explain how you know.
 Find the surface area of this polyhedron. Show your reasoning.
Solution
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Problem 4

A parallelogram has a base of 12 meters and a height of 1.5 meters. What is its area?
 A triangle has a base of 16 inches and a height of \(\frac18\) inches. What is its area?
 A parallelogram has an area of 28 square feet and a height of 4 feet. What is its base?
 A triangle has an area of 32 square millimeters and a base of 8 millimeters. What is its height?
Solution
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(From Unit 1, Lesson 8.)Problem 5
Find the area of the shaded region. Show or explain your reasoning.
Solution
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(From Unit 1, Lesson 3.)