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9.2

9.2. Essential Question: How do you Calculate the Surface Area of Prisms & Cylinders?. Surface Area. Sum of all the areas of the faces of a polyhedron i.e. Calculate the area of each face using the formulas for area of polygon and then add them together. Example 1. Use the Net of a Prism.

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9.2

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  1. 9.2 Essential Question: How do you Calculate the Surface Area of Prisms & Cylinders?

  2. Surface Area • Sum of all the areas of the faces of a polyhedron • i.e. Calculate the area of each face using the formulas for area of polygon and then add them together.

  3. Example 1 Use the Net of a Prism Find the surface area of the rectangular prism. 15 40 24 24 40 15

  4. Example 1 Use the Net of a Prism Find the surface area of the rectangular prism. SOLUTION Add the areas of all the rectangles that form the faces of the prism.

  5. Example 1 Use the Net of a Prism Add the areas of all the faces to get the surface area. S = 40 + 40 + 24 + 24 + 15 + 15 Add the area of all six faces. = 158 Simplify. The surface area of the prism is 158 square inches. ANSWER

  6. Example 2 Find Surface Area of a Prism Find the surface area of the prism.

  7. Example 2 Find Surface Area of a Prism Find the surface area of the prism. Triangles: 2 A = ½ bh = ½ (3)(4) = 6 2 Triangles = 6 times 2 = 12 Rectangle A = (4)(2)=8 A = 3 * 2 = 6 A = 5 * 2 = 10 8 + 6 + 10 = 24 SA = 12 + 24 = 36 m2

  8. Surface Area of a Prism SA = 2BA+PBh Where B = area of the base and P = the perimeter of the base

  9. Example 2 Find Surface Area of a Prism Find the surface area of the prism. SOLUTION 1 Find the area of a triangular base. 1. 2 BA= · 4 · 3 = 2 · 3 = 6 Find the perimeter of a base. 2. PB = 3 + 4 + 5 = 12 Find the height of the prism. In the diagram, h=2. 3.

  10. Example 2 Find Surface Area of a Prism S = 2BA +PBh Formula for the surface area of a prism = 2 ·6 + 12·2 Substitute 6 for B, 12 for P, and 2 for h. = 12 +24 Multiply. = 36 Add. Use the formula for surface area of a prism. 4. The surface area of the prism is 36 square meters. ANSWER

  11. Checkpoint Find Surface Area of Prisms Find the surface area. 1. 2. 3.

  12. Checkpoint Find Surface Area of Prisms Find the surface area of the prism. 1. 2. 72 in.2 236 ft2 144 cm2 ANSWER ANSWER ANSWER 3.

  13. Surface Area of A Cylinder SA = 2BA +PBh SA = 2πr2 +2πrh SA = 2B + Ph

  14. Example 3 Find Surface Area of a Cylinder Find the surface area of the cylinder. Round your answer to the nearest whole number. SOLUTION The radius of the base is 3 feet and the height 4 feet. Use these values in the formula for surface area of a cylinder. S = 2πr2 +2πrh Write the formula for surface area. = 2π(32) +2π(3)(4) Substitute 3 for r, and 4 for h. = 18π +24π Simplify. = 42π Add. ≈ 132 Multiply. The surface area is about 132 square feet. ANSWER

  15. Checkpoint Find Surface Area of Cylinders Find the area described. Round your answer to the nearest whole number. surface area 4. surface area 5. lateral area 6.

  16. Checkpoint Find Surface Area of Cylinders Find the area described. Round your answer to the nearest whole number. surface area 4. surface area 5. 13 m2 151 in.2 603 ft2 ANSWER ANSWER ANSWER lateral area 6.

  17. 1. The solid is not a polyhedron. ANSWER 2. The solid is a polyhedron with congruent triangular bases in parallel planes, so it is a triangular prism. ANSWER Review: Tell whether the solid is a polyhedron. If so, identify the shape of the bases. Then name the solid.

  18. 3. Name the polyhedron. Count the number of faces and edges and then list the congruent faces and congruent edges. ANSWER NJ MJ PN NM pentagonal pyramid; 6 faces, 10 edges; congruent faces: ∆PJN ∆NJM  ∆MJL  ∆LJK ∆KJP; congruent edges:     ,     KJ KP LJ PJ ML LK

  19. Worksheet 9.2A

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