1. Surface Area and Volume of Pyramids Goal: Students will find the surface area and volume of pyramids.

2. Surface Area of Pyramids A pyramid is a polyhedron in which the base is a polygon and the lateral faces are triangles with a common vertex, called the vertex of the pyramid. The intersection of two lateral faces is a lateral edge. The intersection of the base and a lateral face is a base edge.

3. The height of the pyramid is the perpendicular distance between the base and the vertex, called the altitude.

4. Regular Pyramid A regular pyramid has a regular polygon for a base, and the segment joining the vertex and the center of the base is perpendicular to the base. The lateral faces of a regular pyramid are congruent isosceles triangles.

5. The slant height, l, of a regular pyramid is the height of a lateral face of the regular pyramid. Ex.1: A regular square pyramid has a height of 15 centimeters and a base edge length of 16 centimeters. Find the area of each lateral face of the pyramid.

6. The lateral area of a pyramid is the sum of the areas of the congruent lateral faces. The surface area of a pyramid is when the area of the base is added to its lateral area.

7. Theorem 12.4 Surface Area of a Regular Pyramid: Lateral Area: L.A. = Surface Area: where p is the perimeter of the base, l is the slant height, and B is the area of the base.

8. Ex.2: Find the surface area of the regular pyramid. Ex.3: Find the surface area of the regular pyramid.

9. Ex.4: Find the surface area of the regular pyramid. Ex.5: Find the surface area of the regular pyramid.

10. Volume of Pyramids Theorem 12.9 Volume of a Pyramid: Volume: where B is the area of the base, h is the height of the pyramid.

11. Ex.6: Find the volume of the solid. Ex.7: Find the volume of a regular square pyramid with base edges 40 feet long and slant height 25 feet.

12. Ex.8: Originally, the pyramid had height 144 meters and volume 2, 226, 450 cubic meters. Find the side length of the square base.

13. Ex.9: Find the volume of the solid shown.

14. Ex.10: Find the surface area of the solid shown.