3-Dimentional Figures Section 11.1

Warm Up Classify each polygon. 1. a polygon with three congruent sides 2. a polygon with six congruent sides and six congruent angles 3. a polygon with four sides and with opposite sides parallel and congruent

A 3-D figure is called a Solid. The flat surfaces of a solid are called faces. The line segments where the faces intersect are called edges. The point where the edges meet is called a vertex. The surface area of a 3D figures is the sum of the areas of all the faces.

Application. The goal of creating most sports equipment is to have a very small surface area. This reduces friction with other objects in contact. Reduced friction allows objects to move faster. Spheres have the smallest surface area. This is why balls are used in most sports and why baseball bats are in a round shape.

A cube is a prism with six square faces A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.

Polyhedron Bases: lie in parallel planes. A polyhedron is a solid made up of flat surfaces that are polygons. Each polyhedron is made up of bases and lateral faces. Bases: lie in parallel planes. Lateral Faces: connected faces that are not the bases.

In a prism, the two parallel faces are called bases. The other faces are called lateral faces (they are all parallelograms) that meet at lateral edges. In a pyramid, all of the faces except one intersect at a common point called the vertex. The faces that meet are called lateral faces. They are all triangles. The other face is called the base.

Oblique Prism: A prism with bases that are not aligned one directly above the other.

Oblique Pyramid: The center of the base and vertex do NOT line up.

Classify the figure. State how many and name the vertices, edges, and bases.

Classify the figure. State how many and name the vertices, edges, and bases.

Net Taking apart a 3D figure results in a 2D figures called a net.

Describe the three-dimensional figure that can be made from the given net.

Describe the three-dimensional figure that can be made from the given net.

A cross section is the intersection of a three-dimensional figure and a plane.

Describe the cross section.

Describe the cross section.

Regular Polyhedrons A polyhedron is regular if all of its faces are shaped like congruent regular polygons. Since all of the faces of a regular polyhedron are regular and congruent, all of the edges of a regular polyhedron are congruent. There are exactly five regular polyhedrons. These are called the Platonic Solids.

tetrahedron octahedron hexahedron

icosahedron dodecahedron

Lesson Quiz: Part I 1. Classify the figure. State how many and name the vertices, edges, and bases.

Lesson Quiz: Part II 2. Describe the three-dimensional figure that can be made from this net.

Lesson Quiz: Part III 3. Describe the cross section.