Surface Area Geometry and andMeasurement

Measurement Rectangular Prism Rectangular Prism Surface Area: sum of the areas of all of the faces 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 (A 1 = wh) and 2 lateral faces are 5 cm by 7 cm (A 2 = lh). There are 2 bases 6 cm by 5 cm (A 3 = lw) Example: There are 4 lateral faces: 2 lateral faces are 6 cm by 7 cm (A 1 = wh) and 2 lateral faces are 5 cm by 7 cm (A 2 = lh). There are 2 bases 6 cm by 5 cm (A 3 = lw) A 1 = (6 cm)(7 cm) = 42 cm 2 A 1 = (6 cm)(7 cm) = 42 cm 2 A 2 = (5 cm)(7 cm) = 35 cm 2 A 2 = (5 cm)(7 cm) = 35 cm 2 A 3 = (6 cm)(5 cm) = 30 cm 2 A 3 = (6 cm)(5 cm) = 30 cm 2 SA rectangular prism = 2wh + 2lh + 2lw SA rectangular prism = 2wh + 2lh + 2lw SA = 2(42 cm 2 ) + 2(35 cm 2 ) + 2(30 cm 2 ) SA = 2(42 cm 2 ) + 2(35 cm 2 ) + 2(30 cm 2 ) SA = 84 cm cm cm 2 SA = 84 cm cm cm 2 SA = 214 cm 2 SA = 214 cm 2 7 cm 6 cm 5 cm

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

Measurement Triangular Prism Triangular Prism Surface Area: sum of the areas of all of the faces Surface Area: sum of the areas of all of the faces Example: There are 3 lateral faces: 6 m by 7 m (A 1 = bl). There are 2 bases: 6 m for the base and 5 m for the height (2A 2 = bh). Example: There are 3 lateral faces: 6 m by 7 m (A 1 = bl). There are 2 bases: 6 m for the base and 5 m for the height (2A 2 = bh). A 1 = (6 m)(7 m) = 42 m 2 A 1 = (6 m)(7 m) = 42 m 2 2A 2 = (6 m)(5 m) = 30 m 2 2A 2 = (6 m)(5 m) = 30 m 2 SA triangular prism = bh + 3bl SA triangular prism = bh + 3bl SA = 30 m 2 + 3(42 m 2 ) SA = 30 m 2 + 3(42 m 2 ) SA = 30 m m 2 SA = 30 m m 2 SA = 156 m 2 SA = 156 m 2 7 m 6 m 5 m

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

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

Measurement Triangular Pyramid Triangular Pyramid Square Pyramid Square Pyramid