1. Surface Areas 8.7 Surface Area

2. Objective Apply the surface area formula to various 3-dimensional figures in order to find the area 8.7 Surface Area

3. A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at the vertex of the pyramid. Base Lateral Face Vertex 8.7 Surface Area

4. The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base. The length of the altitude is the height h of the pyramid. h 8.7 Surface Area

5. A regular pyramid is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. The slant height l is the length of the altitude of the lateral faces of the pyramid. h pentagonal pyramid Slant Height 8.7 Surface Area

6. What is the shape of each lateral face? How many lateral faces exist? What is the area of one lateral faces? What is the lateral area? h pentagonal pyramid 8.7 Surface Area

7. What is the shape of the base? What is the area of the base? What is the surface area? h pentagonal pyramid 8.7 Surface Area

8. Theorem 10-3 Lateral and Surface Areas of a Regular Pyramid The lateral area of a regular pyramid is half the product of the perimeter of the base and the slant height. L.A. = 1 / 2 pl The surface area of a regular pyramid is the sum of the lateral area and the areas of the base. S.A. = L.A. + B 8.7 Surface Area

9. Find the lateral area and surface area. L.A. = 1 / 2 pl S.A. = L.A. + 2B 8.7 Surface Area

10. Find the lateral area and surface area. L.A. = 1 / 2 pl S.A. = L.A. + 2B 8.7 Surface Area

11. A cone is “pointed” like a pyramid, but its base is a circle. In a right cone, the altitude is a perpendicular segment from the vertex to the center of the base. 8.7 Surface Area

12. The height h is the length of the altitude. The slant height l is the distance from the vertex to a point on the edge of the base. 8.7 Surface Area

13. Theorem 10-4 Lateral and Surface Areas of a Cone The lateral area of a right cone is half the product of the circumference of the base and the slant height. L.A. = ½  2πr  l or L.A. = πrl The surface area of a right cone is the sum of the lateral area and the areas of the base. S.A. = L.A. + B (B = area of the base, or πr 2 ) 8.7 Surface Area

14. Find the lateral area and surface area. 8.7 Surface Area

15. Find the lateral area and surface area. 8.7 Surface Area

16. A soup can is made of metal and covered with a paper label. If the radius of the bottom of the soup can is 4 inches and the height is 5 inches, find the following: The surface area of metal used in an unopened can. The area of paper used in the label. The area of metal remaining once the lid has been thrown away. 8.7 Surface Area

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