Lesson 13

Polyhedra

Let’s investigate polyhedra.

Problem 1

Select all the polyhedra.

Figure A rectangular pyramid. Figure B many sided polyhedron. Figure C cone. Figure D Prism with hexagon faces. Figure E sphere.
A:

A

B:

B

C:

C

D:

D

E:

E

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

Tyler said this net cannot be a net for a square prism because not all the faces are squares.

Do you agree with Tyler? Explain your reasoning.

net. 4 adjacent rectangles. Square above rectangle 2 and beow rectangle 1.

Problem 4

Explain why each of these triangles has an area of 9 square units.

Three triangles labeled A, B, and, C. Each triangle has a bas of 6 units and a height of 3 units.
(From Unit 1, Lesson 8.)

Problem 5

  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 9.)

Problem 6

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.)