1. Chapter 11: Surface Area and Volume Section 11-3: Surface Areas of Pyramids and Cones

2. Objective: To calculate the surface area of pyramids and cones.

3. Pyramid A pyramid is a polyhedron in which the base is a polygon and all lateral faces are triangles which meet at a vertex. A regular pyramid is a pyramid whose base is a regular polygon. The slant height is the length of the altitude of the lateral face.

4. Theorem 11-3: Lateral and Surface Area of a Pyramid The lateral area of a pyramid is the sum of the areas of the congruent lateral faces. The surface area of a pyramid is the lateral area plus the area of the base.

5. Example Find the lateral area Find the surface area

6. Cone A cone is a “pointed” like pyramid. The base of a cone is a circle. In a right cone, the altitude is the perpendicular segment from the vertex to the center of the base. The height is length of the altitude. The slant height l is the distance from the vertex to a point on the edge of the base.

7. Theorem 11-4: 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. LA= p rl The surface area of a right cone is equal to the sum of the lateral area and the area of the base.

8. Example Find the lateral area Find the surface area