1. 10.4 Surface Area of Prisms and Cylinders
Geometry

2. Definitions: Lateral face: not the base
Lateral edge: not an edge of the base
Right prism: All lateral faces are rectangles
Oblique prism: has at least one nonrectangular lateral face

3. Diagram:

4. Definitions
Altitude: the perpendicular segment joining the planes of the bases (the height of the prism)

5. Definition
Surface Area: the total area of all faces and curved surfaces of a three-dimensional figure.

6. Formulas Lateral Area of Right Prisms L=Ph
Surface Area of Right Prisms
S=L+2B or
S=Ph+2B

7. Examples:
Find the lateral area and surface area of the right prism.

8. Example:
Find the lateral area and surface area of a right regular triangular prism with height 20 cm and base edges 10 cm.

9. Example:
Find the lateral and surface area of a cube with edge length 8 cm.

10. Definitions:
Lateral surface: cylinder is the curved surface that connects the two bases.
Axis of a cylinder: the segment with endpoints at the centers of the bases.(also called height)
Right Cylinder: the axis is perpendicular to the bases
Obliques Cylinder: the axis is not perpendicular to the bases.

11. Diagram:

12. Formulas:

13. Example:
Find the lateral and surface area for the right cylinder.

14. Example:

15. Example:

16. Examples:
Find the surface area of the composite figure.

17. Example:
Find the surface area of the composite figure.

18. Example:
The edge length of the cube is tripled. Describe the effect on the surface area.

19. Example:
The height and the diameter of the cylinder are multiplied by ½ . Describe the effect on the surface area.

20. Example:
A sporting goods company sells tents in two styles, shown below. The sides and floor of each tent are made of nylon. Which tent requires less nylon to manufacture?