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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

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Holt CA Course 1 10-7 Three-Dimensional Figures Vocabulary polyhedron face edge vertex cube base

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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.

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Holt CA Course 1 10-7 Three-Dimensional Figures Additional Example 1: Identifying Faces, Edges, and Vertices Identify the number of faces, edges, and vertices on each three-dimensional figure. A. B. 5 faces8 edges5 vertices7 faces15 edges10 vertices

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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 faces12 edges8 vertices5 faces9 edges6 vertices

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Holt CA Course 1 10-7 Three-Dimensional Figures Two 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.

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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

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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.

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Holt CA Course 1 10-7 Three-Dimensional Figures

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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.

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Holt CA Course 1 10-7 Three-Dimensional Figures Additional 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.

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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.

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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.

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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.

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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.

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