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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

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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.

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**Additional Example 1: Naming Prisms and Pyramids**

Identify the bases and faces of the figure. Then name the figure. A. There is one base, and it is a pentagon. There are five triangular faces. The figure is a pentagonal pyramid.

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**Additional Example 1: Naming Prisms and Pyramids**

Describe the bases and faces of the figure. Then name the figure. B. There is one base, and it is a triangle. There are three triangular faces. The figure is a triangular pyramid.

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**Additional Example 1: Naming Prisms and Pyramids**

Describe the bases and faces of the figure. Then name the figure. C. There are two bases, and they are both hexagons. There are six rectangular faces. The figure is a hexagonal prism.

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Check It Out! Example 1 Describe the bases and faces of the figure. Then name the figure. A. There are two bases and they are both triangles. There are three rectangular faces. The figure is a triangular prism.

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Check It Out! Example 1 Describe the bases and faces of the figure. Then name the figure. B. There are two rectangular bases. There are four other rectangular faces. The figure is a rectangular prism.

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Check It Out! Example 1 Describe the bases and faces of the figure. Then name the figure. C. There are two octagonal bases. There are eight rectangular faces. The figure is an octagonal prism.

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**Other three-dimensional figures include cylinders and cones**

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

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**Additional Example 2: Classifying Three-Dimensional Figures**

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

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**Additional Example 2: Classifying Three-Dimensional Figures**

Classify each figure as a polyhedron or not a polyhedron. Then name the figure. B. The faces are not all polygons, so the figure is not a polyhedron. There is one circular base. The figure is a cone.

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**Additional Example 2: Classifying Three-Dimensional Figures**

Classify each figure as a polyhedron or not a polyhedron. Then name the figure. C. The faces are not all polygons, so the figure is not a polyhedron. There are two circular bases. The figure is a cylinder.

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Check It Out! Example 2 Classify each figure as a polyhedron or not a polyhedron. Then name the figure. A. The faces are not all polygons, so the figure is not a polyhedron. There is one circular base for the top figure and two circular bases for the bottom figure. The figure is made up of a cylinder and a cone.

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Check It Out! Example 2 Classify each figure as a polyhedron or not a polyhedron. Then name the figure. B. The faces are all polygons, so the figure is a polyhedron. There are two triangular bases for the figure. The figure is a triangular prism.

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Check It Out! Example 2 Classify each figure as a polyhedron or not a polyhedron. Then name the figure. C. The faces are all polygons, so the figure is a polyhedron. There is one square base for the figure. The figure is a square pyramid.

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