1. Surface Area of Pyramids Lesson 12.2

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.

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

4. 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:

5. 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 = ½bh = ½(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 = 192 + 144 = 336 units 2

6. 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 = 2250 50 ft45 ft Find the area of the triangular sides.

7. Find the slant height of the triangle with base of 45. 40 ft 25 ft 40 2 + 25 2 = slant height 2 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 units 2 50 ft 45 ft Find the slant height of the triangle with base of 50. 40 ft 22.5 ft 40 2 + 22.5 2 = 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 units 2 45 ft 50 ft Total Area = 2,250 + 2,122.6 + 2,294.7 = 6,667.3 units 2

8. 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: 12 2 + 5 2 = slant height 2 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: 2 2 + 1.5 2 = slant height 2 Slant height = 2.5 Find area of 4 triangles: A = 4(½)(3)(2.5) = 15 Surface Area of shaded part = 360-15 = 345 units 2