12 2 Surface Areas of Pyramids OBJECTIVE AFTER

12. 2 Surface Areas of Pyramids OBJECTIVE AFTER STUDYING THIS SECTION, YOU WILL BE ABLE TO FIND THE SURFACE AREAS OF PYRAMIDS

Pyramids A pyramid has only one base. Its lateral edges are not parallel but meet at a single point called the vertex. The base may be any polygon, but the lateral faces will always be triangles. We name pyramids by their base.

Regular Pyramids A regular pyramid has a regular polygon as its base and also has congruent lateral edges. The lateral faces of a regular pyramid are congruent isosceles triangles.

Parts of Pyramids Slant height - the height of a lateral face. altitude- the perpendicular segment from the vertex to the base. (The foot of the altitude is the center of the base. ) A regular pyramid’s slant height and altitude determine a right triangle. The altitude and a lateral edge determine a right triangle.

Example 1 Given the regular pyramid shown Find a. the lateral area (L. A. ) b. the total area (T. A. ) 10 12

Example 2 The base of rectangular pyramid ABCDE is 10 by 18. The altitude is 12. The lateral edges are congruent. A. Why is ABCDE not a regular pyramid? B. Find the pyramid’s total surface area. A E B D F C

Summary What is the difference between altitude and slant height of a regular pyramid? Homework: worksheet