Surface area of Pyramids and cones

1. 12-3 Surface area of Pyramids and cones

2. Pyramids • 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 a common vertex (called the vertex of the pyramid)

3. Pyramid Parts • The altitude of a pyramid is the perpendicular segment from the vertex (also called apex) to the plane of the base. • The length of the altitude is the height (h) of the pyramid.

4. Pyramid Parts Cont. • A regular pyramid is a pyramid whose base is a regular polygon. • The lateral faces are congruent isosceles triangles. • The slant height (l) is the length of the altitude of a lateral face of the pyramid.

5. Vertex or apex

6. Lateral Area • The lateral area is the sum of the areas of the congruent lateral faces. • Let’s work it out.

7. l 9090 Lateral Face base s

8. Lateral Areas of Regular Pyramids • The lateral area of a regular pyramid is half the product of the perimeter of the base and the slant height. L.A. = ½ pl

9. Surface area of a Regular Pyramid • The surface area of a regular pyramid is the sum of the lateral area and the area of the base (B). S.A. = L.A. + B = ½ pl + B

10. Cones • A cone is 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. • 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

11. Right cone l

12. Lateral Area of a Right 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 = πrl

13. Surface Area of a Right Cone • The surface area of a right cone is the sum of the lateral area and the area of the base. S.A. = L.A. + B = πrl +πr2

14. Joke time • What do you get when you cross geometry and McDonald’s? • A plane cheeseburger

15. Joke time • Why was the obtuse angle upset? • Because he was never right.