Three-Dimensional Figures Polyhedrons

Geometry HS Mathematics Unit: 09 Lesson: 01 Three-Dimensional Figures: Polyhedrons

Geometric solids have three dimensions — ______

Types of geometric solids:

______– solid formed by polygons that enclose a region of space. The flat polygonal surfaces are called faces. The line segment where two faces meet is called an edge. The point of intersection of three or more edges is called a vertex.

______

triangular prism octahedron cylinder

______

______– type of polyhedron with two faces called bases, which are congruent, parallel polygons. Lateral faces are parallelograms connecting the bases. In right prisms lateral edges are perpendicular to the bases. A prism that is not a right prism is called an oblique prism. The altitude of any prism is the perpendicular distance from one base to the plane containing the other base.

______

Cube Oblique triangular prism

Geometry HS Mathematics Unit: 09 Lesson: 01 Three-Dimensional Figures: Polyhedrons

Examples:

L M A B D R C W Q N

E H S V P F G O T U

Guided Practice

1. Name the bases of the two prisms. The bases are shaded.

a. Right rectangular prism b. Right hexagonal prism

2. Name the lateral faces of the two prisms.

a. Right rectangular prism b. Right hexagonal prism

3. Name the edges of the two prisms.

a. Right rectangular prism b. Right hexagonal prism

4. Name an altitude of the two prisms.

a. Right rectangular prism b. Right hexagonal prism

Geometry HS Mathematics Unit: 09 Lesson: 01 Three-Dimensional Figures: Polyhedrons

______- type of polyhedron with only one base whose lateral faces meet at a common vertex. D Examples: V R

E H T P Y

Z C O U X T S F G

Guided Practice

5. Name the base of the three pyramids. The bases are shaded.

a. Triangular b. Square c. Trapezoidal

6. Name the lateral faces of the three pyramids.

a. Triangular b. Square c. Trapezoidal

7. Name the edges of the three pyramids.

a. Triangular b. Square c. Trapezoidal

8. Name an altitude of the three pyramids.

a. Triangular b. Square c. Trapezoidal

Geometry HS Mathematics Unit: 09 Lesson: 01 Three-Dimensional Figures: Polyhedrons

Practice Problems

1. Polyhedrons can be classified by number of sides, ______hedron. The prefixes are the same as used for polygons, with one exception. A polyhedron with four faces is called a tetrahedron. Name the following polyhedrons. a. b. c.

2. What are two other names for a cube?

3. Given the following figures, answer the questions. Bases are shaded.

A M H 1.5 mm 18 in. B G L 12 in. C F 4.25 mm N

D E 3.5 mm P O a. Name the prism. b. Name the bases of the prism. c. Name the lateral faces of the prism. d. Name the edges of the prism. e. What is the altitude of the prism? f. Name the pyramid. g. Name the base of the pyramid. h. Name the lateral faces of the pyramid. i. Name the vertex of the pyramid. j. Name the lateral edges of the pyramid. k. What is the height of the pyramid?