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Understanding Prisms in Geometry: Bases, Lateral Faces, and Volume

Learn the fundamentals of prisms, including base types, lateral faces, and volume calculations. Discover the properties and classifications of prisms with examples like rectangular, triangular, and pentagonal prisms.

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Understanding Prisms in Geometry: Bases, Lateral Faces, and Volume

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  1. Section 12-1 Prisms

  2. Prism • a 3-dimensional figure with two congruent, parallel faces • The congruent, parallel faces are called the bases. • The bases lie in parallel planes.

  3. Base Base

  4. Altitude of a prism • a segment joining the two base planes; it is perpendicular to both planes • The length of the altitude is the height of the prism!

  5. altitude

  6. Lateral faces of a prism • the faces that are not its bases • In the shape of parallelograms

  7. Lateral Edges • the parallel segments where adjacent lateral faces intersect

  8. Types of prisms • Right Prism: • have rectangles for the lateral faces • Lateral edges are altitudes • Oblique prism: • Lateral edges are NOT altitudes

  9. Height Example of a Right Prism: Example of an Oblique Prism:

  10. A prism is named by the shape of its base.

  11. Base Base Some Examples of Right Prisms: Rectangular Prism:

  12. If the edges have equal length then the rectangular prism is called a cube.

  13. Base Base Base Base Triangular Prism: : Pentagonal Prism

  14. Base Base Hexagonal Prism: And the list goes on…..

  15. Lateral area • The sum of the areas of the lateral faces

  16. Theorem 12-1 • The lateral area of a right prism equals the perimeter of a base times the height of the prism. L.A. = Ph

  17. T.A. = L.A. + Total Area Area of a Base Lateral Area # of Bases Total Area • The sum of the areas of all its faces

  18. volume • The number of cubic units enclosed by a three dimensional object. Therefore volume is measured in cubic units.

  19. Theorem 12-2 • The volume of a right prism equals the area of a base times the height of the prism.

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