Surface Area of Pyramids Lesson 12.2 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. The base is a regular polygon. Sides are congruent isosceles triangles. Regular Pyramids: Slant height (altitude of lateral surface) altitude of pyramid Vertex to the center of the base is the altitude of the pyramid. Parts of a Pyramid: Find the lateral area & total area of the pyramid. Lateral Area Find the area of the 4 congruent isosceles triangles. Find slant height. 8 A = bh = (12)(8) = 48 LA = 4(48) = 192 units 2 Total Area Equals area of the base plus lateral area. Base is a square. Area = 12(12) = 144 TA = = 336 units 2 Find the surface area of the given pyramid. The base is 45ft by 50ft and the overall height is 40ft. 50 ft 45 ftBase Area of base = 45(50) Area of base = ft45 ft Find the area of the triangular sides. Find the slant height of the triangle with base of ft 25 ft = slant height 2 1, = 2,225 Slant height = 589 A = bh A = (45)(589) A = 89 2 triangles = 2(112.5 89) = 225 89 = 2,122.6 units 2 50 ft 45 ft Find the slant height of the triangle with base of ft 22.5 ft = slant height 2 1, = 2, Slant height = A = bh A = (50)( ) A = 25 triangles = 2(25 ) = 50 = 2,294.7 units 2 45 ft 50 ft Total Area = 2, , ,294.7 = 6,667.3 units 2 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: = slant height 2 Slant height = 13 Find area of 4 triangles: A = 4()10(13) A = 260 Total Area = = 360 Find the area of the triangles at the top pyramid: Slant height: = slant height 2 Slant height = 2.5 Find area of 4 triangles: A = 4()(3)(2.5) = 15 Surface Area of shaded part = = 345 units 2