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11.1 Space Figures and Cross Sections

11.1 Space Figures and Cross Sections. A polyhedron is a space figure, or three-dimensional figure, whose surfaces are polygons. Each polygon is a face of the polyhedron. An edge is a segment that is formed by the intersection of two faces.

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11.1 Space Figures and Cross Sections

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  1. 11.1 Space Figures and Cross Sections • A polyhedron is a space figure, or three-dimensional figure, whose surfaces are polygons. • Each polygon is a face of the polyhedron. • An edge is a segment that is formed by the intersection of two faces. • A vertex is a point where three or more edges intersect.

  2. Identifying Vertices, Edges, and Faces • How many vertices, edges, and faces are in the polyhedron? List them. • Vertices: D, E, F, G, H • Edges: • Faces: Quadrilateral DEFG,

  3. Euler’s Formula • Leonhard Euler – a Swiss Mathematician – discovered relationship among the number of faces, vertices, and edges of any polyhedron. • Known as Euler’s Formula • The sum of the number of faces (F) and the vertices (V) of a polyhedron is two more than the number of its edges (E). F + V = E + 2

  4. Using Euler’s Formula • How many vertices, edges, and faces does the polyhedron have? Use your results to verify Euler’s Formula. F = 8 V = 12 E = 18 F + V = E + 2 8 + 12 = 18 + 2 20 = 20

  5. Cross Section • A cross section is the intersection of a solid and a plane. • Can think of a cross section as a very thin slice of the solid.

  6. Describing a Cross Section • What is the cross section formed by the plane and the solid? • The cross section is a rectangle.

  7. More Practice!!!!! • Homework – Textbook p. 692 #6 – 20 ALL.

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