Holt CA Course 1

10-1 Three-Dimensional Figures

Warm UpWarm Up

California StandardsCalifornia Standards

Lesson Presentation

PreviewPreview

Holt CA Course 1

10-1 Three-Dimensional Figures

Warm UpIdentify each two-dimensional figure described.

1. four sides that are all congruent

2. six sides

3. four sides with parallel opposite sides

4. four right angles and four congruent sides

rhombus

hexagon

parallelogram

square

Holt CA Course 1

10-1 Three-Dimensional Figures

Preparation for MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

California Standards

Holt CA Course 1

10-1 Three-Dimensional Figures

Vocabulary

faceedgepolyhedronvertexbase

prism

pyramidcylindercone

Holt CA Course 1

10-1 Three-Dimensional Figures

Three-dimensional figures have three-dimensions: length, width, and height. A flat surface of a three-dimensional figure is a face. An edge is where two faces meet.

A polyhedron is a three-dimensional figure whose faces are all polygons. A vertex of a polyhedron is a point where three or more edges meet. The face that is used to name a polyhedron is called a base.

Holt CA Course 1

10-1 Three-Dimensional Figures

Holt CA Course 1

10-1 Three-Dimensional Figures

Additional Example 1: Naming Prisms and Pyramids

There is one base, and it is a pentagon.

There are five triangular faces.

The figure is a pentagonal pyramid.

Identify the bases and faces of the figure. Then name the figure.

A.

Holt CA Course 1

10-1 Three-Dimensional Figures

Additional Example 1: Naming Prisms and Pyramids

There is one base, and it is a triangle.

There are three triangular faces.

The figure is a triangular pyramid.

Describe the bases and faces of the figure. Then name the figure.

B.

Holt CA Course 1

10-1 Three-Dimensional Figures

Additional Example 1: Naming Prisms and Pyramids

There are two bases, and they are both hexagons.

There are six rectangular faces.

The figure is a hexagonal prism.

Describe the bases and faces of the figure. Then name the figure.

C.

Holt CA Course 1

10-1 Three-Dimensional Figures

Check It Out! Example 1

There are two bases and they are both triangles.

There are three rectangular faces.

The figure is a triangular prism.

Describe the bases and faces of the figure. Then name the figure.

A.

Holt CA Course 1

10-1 Three-Dimensional Figures

Check It Out! Example 1

There are two rectangular bases.

The figure is a rectangular prism.

Describe the bases and faces of the figure. Then name the figure.

B.

There are four other rectangular faces.

Holt CA Course 1

10-1 Three-Dimensional Figures

Describe the bases and faces of the figure. Then name the figure.

C.

Check It Out! Example 1

There are two octagonal bases.

The figure is an octagonal prism.

There are eight rectangular faces.

Holt CA Course 1

10-1 Three-Dimensional Figures

Other three-dimensional figures include cylinders and cones. These figures are not polyhedrons because they are not made of faces that are all polygons.

Holt CA Course 1

10-1 Three-Dimensional Figures

You can use properties to classify three-dimensional figures.

Holt CA Course 1

10-1 Three-Dimensional Figures

Classify each figure as a polyhedron or not a polyhedron. Then name the figure.

A.

Additional Example 2: Classifying Three-Dimensional Figures

The faces are all polygons, so the figure is a polyhedron.There is one rectangular base for each figure.

The figure is made up of a rectangular pyramid and a rectangular prism.

Holt CA Course 1

10-1 Three-Dimensional Figures

There is one circular base.

Classify each figure as a polyhedron or not a polyhedron. Then name the figure.

B.

Additional Example 2: Classifying Three-Dimensional Figures

The faces are not all polygons, so the figure is not a polyhedron.

The figure is a cone.

Holt CA Course 1

10-1 Three-Dimensional Figures

There are two circular bases.

Classify each figure as a polyhedron or not a polyhedron. Then name the figure.

C.

Additional Example 2: Classifying Three-Dimensional Figures

The faces are not all polygons, so the figure is not a polyhedron.

The figure is a cylinder.

Holt CA Course 1

10-1 Three-Dimensional Figures

Check It Out! Example 2

Classify each figure as a polyhedron or not a polyhedron. Then name the figure.

A.

There is one circular base for the top figure and two circular bases for the bottom figure.

The faces are not all polygons, so the figure is not a polyhedron.

The figure is made up of a cylinder and a cone.

Holt CA Course 1

10-1 Three-Dimensional Figures

Check It Out! Example 2

Classify each figure as a polyhedron or not a polyhedron. Then name the figure.

B.

There are two triangular bases for the figure.

The faces are all polygons, so the figure is a polyhedron.

The figure is a triangular prism.

Holt CA Course 1

10-1 Three-Dimensional Figures

Check It Out! Example 2

Classify each figure as a polyhedron or not a polyhedron. Then name the figure.

C.

There is one square base for the figure.

The faces are all polygons, so the figure is a polyhedron.

The figure is a square pyramid.

Holt CA Course 1

10-1 Three-Dimensional Figures

Lesson Quiz: Part IDescribe the bases and faces of each figure. Then name each figure.

Two pentagonal bases, 5 rectangular faces; pentagonal prism

One square base, 4 triangular faces; square pyramid

1.

2.

Holt CA Course 1

10-1 Three-Dimensional Figures

Lesson Quiz: Part II

Classify each figure as a polyhedron or not a polyhedron. Then name the figure.

polyhedron, rectangular prism

polyhedron, triangular prism

3.

4.