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**Notes on Intro to 3D Figures**

Essential Question: How would you use Perimeter, Area, Surface Area, and Volume in your backyard? Benchmark: “The student will be able to…” Justify and apply formulas for Surface Area and Volume of pyramids, prisms, cylinders, and cones. Learning Goal: “The student will be able to understand…” Measurement and Geometry Learning Activity: “We will learn this by…” Notes on Intro to 3D Figures

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**A polyhedron is a 3D figure whose faces are all polygons.**

3D figures have three dimensions: length, width, and height. A flat surface of a 3D figure is a face. An edge is where two faces meet. A polyhedron is a 3D figure whose faces are all polygons. The face that is used to name a polyhedron is a base. A prism has two bases, and a pyramid has one.

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

Identify the bases and faces of the figure. Then name the figure. There are two octagonal bases. There are eight rectangular faces. The figure is an octagonal prism.

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

Identify the bases and faces of the figure. Then name the figure. 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 1C: Naming Prisms and Pyramids**

Identify the bases and faces of the figure. Then name the figure. 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 1D: Naming Prisms and Pyramids**

Identify the bases and faces of the figure. Then name the figure. 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 1A Identify the bases and faces of the figure. Then name the figure. 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 1B Identify the bases and faces of the figure. Then name the figure. All faces and bases are congruent squares. The figure is a cube.

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**Other 3D figures include cylinders, cones, and spheres**

Other 3D figures include cylinders, cones, and spheres. These figures are not polyhedrons.

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**You can use properties to classify three- dimensional figures.**

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

Classify each figure as a polyhedron or not a polyhedron. Then name the figure. 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 2B: Classifying Three- Dimensional Figures**

Classify each figure as a polyhedron or not a polyhedron. Then name the figure. 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 2C: Classifying Three- Dimensional Figures**

Classify each figure as a polyhedron or not a polyhedron. Then name the figure. 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 2A Classify each figure as a polyhedron or not a polyhedron. Then name the figure. 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 2B Classify each figure as a polyhedron or not a polyhedron. Then name the figure. 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 2C Classify each figure as a polyhedron or not a polyhedron. Then name the figure. 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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