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Surface Area

Surface Area. Geometry and Measurement. 7 cm. 5 cm. 6 cm. Measurement. Rectangular Prism Surface Area : sum of the areas of all of the faces

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Surface Area

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  1. Surface Area Geometry and Measurement

  2. 7 cm 5 cm 6 cm Measurement • Rectangular Prism • Surface Area: sum of the areas of all of the faces • Example: There are 4 lateral faces: 2 lateral faces are 6 cm by 7 cm (A1= wh) and 2 lateral faces are 5 cm by 7 cm (A2 = lh). There are 2 bases 6 cm by 5 cm (A3 = lw) • A1 = (6 cm)(7 cm) = 42 cm2 • A2 = (5 cm)(7 cm) = 35 cm2 • A3 = (6 cm)(5 cm) = 30 cm2 • SA rectangular prism = 2wh + 2lh + 2lw • SA = 2(42 cm2) + 2(35 cm2) + 2(30 cm2) • SA = 84 cm2 + 70 cm2 + 60 cm2 • SA = 214 cm2

  3. 5 cm Measurement • Cube • Surface Area: sum of the areas of all 6 congruent faces • Example: There are 6 faces: 5 cm by 5 cm (A = s2) • SA cube = 6A = 6s2 • SA = 6(5 cm)2 • SA = 6(25 cm2) • SA = 150 cm2

  4. 7 m 5 m 6 m Measurement • Triangular Prism • Surface Area: sum of the areas of all of the faces • Example: There are 3 lateral faces: 6 m by 7 m (A1= bl). There are 2 bases: 6 m for the base and 5 m for the height (2A2 = bh). • A1 = (6 m)(7 m) = 42 m2 • 2A2 = (6 m)(5 m) = 30 m2 • SA triangular prism = bh + 3bl • SA = 30 m2 + 3(42 m2) • SA = 30 m2 + 126 m2 • SA = 156 m2

  5. 3 ft 12 ft Measurement • Cylinder • Surface Area: area of the circles plus the area of the lateral face • Example: r = 3 ft; h = 12 ft • SA cylinder= 2rh +2r2 • SA = 2 (3 ft)(12 ft) + 2 (3 ft)2 • SA = 72 ft2 + 2 (9 ft2) • SA = 72 ft2 + 18 ft2 • SA = 90 ft2

  6. 8 mm Measurement • Sphere • Surface Area: 4r2 where r is the radius • Example: r = 8 mm • SA sphere = 4r2 • SA = 4(8 mm)2 • SA = 4(64 mm2) • SA = 256 mm2

  7. Measurement • Triangular Pyramid • Square Pyramid

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