CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-2 PYRAMIDS

PYRAMID Much like a prism, a pyramid is a 3- dimensional solid that can have any polygon as a base. A pyramid is different than a prism in that a pyramid only has one base where a prism has two bases. Also, pyramids have lateral faces that are triangles instead of rectangles or parallelograms like a prism.

PYRAMID VOCABULARY All pyramids have the following: 1.A vertex 2.A base 3.An altitude (H) 4.Lateral faces 5.Lateral edges 6.Slant height (l)

VERTEX & BASE OF A PYRAMID The vertex of a pyramid is the single point at which all lateral faces meet. The base of a pyramid can be any polygon. We will focus on pyramids whose bases are regular polygons.

ALTITUDE OF A PYRAMID The altitude (height, h) of a pyramid is the segment drawn from the vertex to the base and is perpendicular to the base.

LATERAL FACES & EDGES OF A PYRAMID The lateral faces of a pyramid are triangles and there are as many lateral faces as there are sides on the base. The lateral edges of a pyramid occur where lateral faces meet.

PYRAMID VERTEX BASE LATERAL EDGELATERAL FACE HEIGHT (H) H

REGULAR PYRAMIDS We will study, in depth, regular pyramids. REGULAR PYRAMIDS have the following qualities: 1.Base is a regular polygon 2.Lateral edges are congruent 3.Lateral faces are congruent isosceles triangles, each with a slant height of the pyramid. 4.The altitude meets the base at its center

SLANT HEIGHT The slant height (l) of a regular pyramid is the height of a lateral face. In a regular pyramid, the height, slant height, and segment of the base that joins the two form a right triangle. Also, the slant height, measure of the lateral edge, and segment of the base of a lateral face form a right triangle.

REGULAR PYRAMID h l

THEOREM 12-3 The lateral area of a regular pyramid equals half the perimeter of the base times the slant height. L.A. = ½ p l

TOTAL AREA OF A PYRAMID Recall that the total area of a solid is the sum of the areas of all faces. A pyramid only has one base, so the formula for total area of a pyramid is: T.A. = L.A. + B

THEOREM 12-4 The volume of a pyramid equals one third the area of the base times the height of the pyramid. V = 1/3 B H

CLASSWORK/HOMEWORK 12.2 ASSIGNMENT Classwork: Pg. 484, Classroom Exercises 2-16 even Homework: Pg. 485, Written Exercises 2-16 even