Surface Area of Pyramids NOTES 12.2 Surface Area of Pyramids

Pyramids: Has only one base (polygon). Edges are not parallel but meet at a single point called the vertex. Lateral faces are triangles named by its base.

Regular Pyramids: The base is a regular polygon. Sides are congruent isosceles triangles.

Parts of a Pyramid: altitude of pyramid Slant height (altitude of lateral surface) Vertex to the center of the base is the altitude of the pyramid.

Find the lateral area & total area of the pyramid. Find the area of the 4 congruent isosceles triangles. Find slant height. 8 A = ½bh = ½(12)(8) = 48 LA = 4(48) = 192 units2 Equals area of the base plus lateral area. Base is a square. Area = 12(12) = 144 TA = 192 + 144 = 336 units2

Find the surface area of the given pyramid. Base 45 ft 50 ft Area of base = 45(50) Area of base = 2250 The base is 45ft by 50ft and the overall height is 40ft. 45 ft 50 ft Find the area of the triangular sides.

Find the slant height of the triangle with base of 45. 1,600 + 625 = 2,225 Slant height = 5√89 A = ½bh A = ½(45)(5√89) A = 112.5 √89 2 triangles = 2(112.5 √89) = 225 √89 = 2,122.6 units2 402 + 22.52 = slant height 2 1,600 + 506.25 = 2,106.25 Slant height = √2106.25 A = ½bh A = ½(50)(√2106.25) A = 25√2106.25 2 triangles = 2(25√2106.25) = 50 √2106.25 = 2,294.7 units2 Total Area = 2,250 + 2,122.6 + 2,294.7 = 6,667.3 units2

Given a square pyramid If b = 10, a = 3, h = 10, & x = 2, find the surface area shaded. Find the area of the base: A = 10(10) = 100 Find the slant height: 122 + 52 = slant height2 Slant height = 13 Find area of 4 triangles: A = 4(½)10(13) A = 260 Total Area = 260 + 100 = 360 Find the area of the triangles at the top pyramid: Slant height: 22 + 1.52 = slant height2 Slant height = 2.5 Find area of 4 triangles: A = 4(½)(3)(2.5) = 15 Surface Area of shaded part = 360-15 = 345 units2