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.

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Presentation transcript:

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.