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Lesson Presentation. Sunshine State Standards. MA.7.G.2.1 Justify and apply formulas for surface area..of…pyramids…and cones. Also MA.7.G.2.2. Vocabulary. regular pyramid slant height of a pyramid slant height of a cone.

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  1. Lesson Presentation

  2. Sunshine State Standards MA.7.G.2.1 Justify and apply formulas for surface area..of…pyramids…and cones. Also MA.7.G.2.2

  3. Vocabulary regular pyramid slant height of a pyramid slant height of a cone

  4. The base of a regular pyramid is a regular polygon, and the faces are congruent isosceles triangles. The diagram shows a square pyramid. The blue dashed line labeled l is the slant height of the pyramid, the distance from the vertex to the midpoint of an edge of the base.

  5. 1 2 S = lw + Pl 1 2 S = (9 • 9) + (36)(10) Additional Example 1A: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. B = lw Substitute. P = 4(9) = 36 S = 81 + 180 Add. S = 261 m2 The surface area is 261 square meters.

  6. 1 2 1 2 S = bh + Pl 1 2 1 2 S = (7)(6) + (21)(8) Additional Example 1B: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. B= ½bh. Substitute. P = 3(7) = 21 S = 21 + 84 Add. S = 105 in2 The surface area is 105 square inches.

  7. 5 m 1 2 S = lw + Pl 3 m 3 m 1 2 S = (3 • 3) + (12)(5) Check It Out: Example 1A Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. B= lw. Substitute. P = 4(3) = 12 S = 9 + 30 Add. S = 39 m2 The surface area is 39 square meters.

  8. 4 in. 1 2 1 2 S = bh + Pl 1 2 1 2 S = (4)(3) + (12)(6) 6 in. 4 in. 4 in. 3 in. Check It Out: Example 1B Find the surface area of the pyramid 1 2 S = B + Pl Use the formula. B= ½bh. Substitute. P = 3(4) = 12 S = 6 + 36 Add. S = 42 in2 The surface area is 42 square inches.

  9. The diagram shows a cone and its net. The blue dashed line is the slant height of the cone, the distance from the vertex to a point on the edge of the base.

  10. Additional Example 2: Finding the Surface Area of a Cone Find the surface area of the cone. Use 3.14 for . S = r2 + rl Use the formula. S ≈ (3.14)(32) + (3.14)(3)(10) Substitute. S ≈ 28.26 + 94.2 Multiply. S ≈ 122.46 Add. The surface area is about 122.46 square centimeters.

  11. Check It Out: Example 2 Find the surface area of the cone. Use 3.14 for . S = r2 + rl Use the formula. S ≈ (3.14)(42) + (3.14)(4)(10) Substitute. S ≈ 50.24 + 125.6 Multiply. S ≈ 175.84 Add. The surface area is about 175.84 square centimeters.

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