Surface Area of Pyramids Lesson 12 2 Pyramids

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.

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. 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

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 45 ft by 50 ft and the overall height is 40 ft. 45 ft 50 ft Find the area of the triangular sides.

Find the slant height of the triangle with base of 45. 40 ft 50 ft Find the slant height of the triangle with base of 50. 40 ft 25 ft 402 + 252 = slant height 1, 600 + 625 = 2, 225 Slant height = 5√ 89 45 ft 2 50 ft 22. 5 ft 402 + 22. 52 = slant height 2 1, 600 + 506. 25 = 2, 106. 25 Slant height = √ 2106. 25 A = ½bh A = ½(45)(5√ 89) A = 112. 5 √ 89 A = ½bh A = ½(50)(√ 2106. 25) A = 25√ 2106. 25 2 triangles = 2(112. 5 √ 89) = 225 √ 89 = 2, 122. 6 units 2 2 triangles = 2(25√ 2106. 25) = 50 √ 2106. 25 = 2, 294. 7 units 2 Total Area = 2, 250 + 2, 122. 6 + 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: 122 + 52 = 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: 22 + 1. 52 = 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