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Holt CA Course 1
10-7 Three-Dimensional Figures
Preparation for MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.
California Standards
Holt CA Course 1
10-7 Three-Dimensional Figures
Vocabularypolyhedronfaceedgevertexcubebase
Holt CA Course 1
10-7 Three-Dimensional Figures
A polyhedron is a three-dimensional object with flat surfaces, called faces, that are polygons.
When two faces of a three-dimensional figure share a side, they form an edge. A point at which three or more edges meet is a vertex (plural: vertices).
A cube is formed by 6 congruent square faces. It has 8 vertices and 12 edges.
Holt CA Course 1
10-7 Three-Dimensional FiguresAdditional Example 1: Identifying Faces, Edges,
and Vertices
Identify the number of faces, edges, and vertices on each three-dimensional figure.
A.
B.
5 faces
8 edges
5 vertices
7 faces
15 edges
10 vertices
Holt CA Course 1
10-7 Three-Dimensional Figures
Check It Out! Example 1
Identify the number of faces, edges, and vertices on each three-dimensional figure.
A.
B.
6 faces
12 edges
8 vertices
5 faces
9 edges
6 vertices
Holt CA Course 1
10-7 Three-Dimensional FiguresTwo types of polyhedrons are prisms and pyramids. Prisms and pyramids are named for the shape of their bases. A base of a three-dimensional figure is a face by which the figure is measured or classified.
Holt CA Course 1
10-7 Three-Dimensional Figures
The bottom face of a prism is not always one of its bases. For example, the bottom face of the triangular prism in Example 1 is not one of its triangular bases.
Helpful Hint
Holt CA Course 1
10-7 Three-Dimensional Figures
Other three-dimensional figures include cylinders and cones. These figures are not polyhedrons because their surfaces are not polygons.
Holt CA Course 1
10-7 Three-Dimensional Figures
Holt CA Course 1
10-7 Three-Dimensional Figures
Additional Example 2A: Naming Three-Dimensional Figures
Name the three-dimensional figure represented by the object.
The figure is not a polyhedron.
There is a curved surface.
The figure represents a cylinder.
There are two congruent, parallel bases.
The bases are circles.
Holt CA Course 1
10-7 Three-Dimensional FiguresAdditional Example 2B: Naming Three-
Dimensional Figures
Name the three-dimensional figure represented by the object.
The figure is a polyhedron.
All the faces are flat and are polygons.
The figure is a triangular pyramid.
There is one base and the other faces are triangles that meet at a point, so the figure is a pyramid. The base is a triangle.
Holt CA Course 1
10-7 Three-Dimensional Figures
Additional Example 2C: Naming Three-Dimensional Figures
Name the three-dimensional figure represented by the object.
The figure is a polyhedron.
All the faces are flat and are polygons.
The figure is a rectangular prism.
There are two congruent, parallel bases, so the figure is a prism. The bases are rectangles.
Holt CA Course 1
10-7 Three-Dimensional Figures
Check It Out! Example 2A
Name the three-dimensional figure represented by the object.
The figure is a polyhedron.
All the faces are flat and are polygons.
The figure is a square pyramid.
There is one base and the other faces are triangles that meet at a point, so the figure is a pyramid. The base is a square.
Holt CA Course 1
10-7 Three-Dimensional Figures
Check It Out! Example 2B
Name the three-dimensional figure represented by the object.
The figure is a polyhedron.
All the faces are flat and are polygons.
The figure is a rectangular prism.
There are two congruent, parallel bases, so the figure is a prism. The bases are rectangles.
Holt CA Course 1
10-7 Three-Dimensional Figures
Check It Out! Example 2C
Name the three-dimensional figure represented by the object.
The figure is not a polyhedron.
There is a curved surface.
The figure represents a cylinder.
There are two congruent, parallel bases.
The bases are circles.