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Perimeter, Area, and Volume

Perimeter, Area, and Volume. Geometry and Measurement. 5 ft. 3 ft. Measurement. Rectangle Perimeter P = 2l + 2w, where l = length and w = width Example: l = 5 ft and w = 3 ft P rectangle = 2l + 2w P = 2(5 ft) + 2(3 ft) P = 10 ft + 6 ft P = 16 ft. 5 ft. 3 ft. Measurement.

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Perimeter, Area, and Volume

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  1. Perimeter, Area, and Volume Geometry and Measurement

  2. 5 ft 3 ft Measurement • Rectangle • Perimeter • P = 2l + 2w, where l = length and w = width • Example: l = 5 ft and w = 3 ft • P rectangle = 2l + 2w • P = 2(5 ft) + 2(3 ft) • P = 10 ft + 6 ft • P = 16 ft

  3. 5 ft 3 ft Measurement • Rectangle • Area • A = lw where l = length and w = width • Example: l = 5 ft and w = 3 ft • A rectangle = lw • A = (5 ft)(3 ft) • A = 15 ft2

  4. 3 ft Measurement • Square • Perimeter • P = 4s, where s = length of a side • Example: s = 3 ft • P square = 4s • P = 4(3 ft) • P = 12 ft

  5. 3 ft Measurement • Square • Area • A = s2 where s = length of a side • Example: s = 3 ft • A square = s2 • A = (3 ft)2 • A = 9 ft2

  6. 4 m 5 m 3 m Measurement • Triangle • Perimeter • P= a + b + c, where a, b, and c are the lengths of the sides of the triangle • Example: a = 3 m; b = 4 m; c = 5 m • P triangle = a + b + c • P = 3 m + 4 m + 5 m • P = 12 m

  7. 4 m 5 m 3 m Measurement • Triangle • Area • A = ½ bh, where b is the base and h is the height of the triangle • Example: b = 3 m; h = 4 m • A triangle = ½ bh • A = ½ (3 m) (4 m) • A = 6 m2

  8. 3 cm Measurement • Circle • Circumference • C circle = d or C = 2r, where d = diameter and r = radius • Example: r = 3 cm • C circle = 2r • C = 2(3 cm) • C = 6 cm

  9. 3 cm Measurement • Circle • Area • A = r2, where r = radius • Example: r = 3 cm • A circle = r2 • A = (3 cm)2 • A = 9 cm2

  10. 7 cm 5 cm 6 cm Measurement • Rectangular Prism • Volume: • V = lwh where l is length; w is width; and h is height • Example: l = 6 cm; w = 5 cm; h = 7 cm • V rectangular prism = Bh = lwh • V = (6 cm)(5 cm)(7 cm) • V = 210 cm3

  11. 5 cm Measurement • Cube • Volume: • V = s3 where s is the length of a side • Example: s = 5 cm • V cube = Bh = s3 • V = (5 cm)3 • V = 125 cm3

  12. 7 m 5 m 6 m Measurement • Triangular Prism • Volume: • V = ½ bhl where b is the base; h is height of the triangle; and l is length of the prism • Example: b = 6 m; h = 5 m; l = 7 m • V triangular prism = Bh = ½ bhl • V = ½ (6 m)(5 m)(7 m) • V = 105 m3

  13. 3 ft 12 ft Measurement • Cylinder • Volume of a Cylinder: V = r2h where r is the radius of the base (circle) and h is the height. • Example: r = 3 ft and h = 12 ft. • V cylinder = Bh = r2h • V = (3 ft)2 (12 ft) • V = (9 ft2)(12 ft) • V = 108 ft3

  14. 13 ft 12 ft 5 ft Measurement • Cone • Volume: V = r2h/3 where r is the radius of the base (circle) and h is the height. • Example: r = 5 ft; h = 12 ft • V cone= r2h/3 • V = [(5 ft)2 12 ft ]/ 3 • V = [(25 ft2)(12 ft)]/3 • V = (25 ft2)(4 ft) • V = 100 ft3

  15. 6 mm Measurement • Sphere • Volume of a Sphere: V = (4/3) r3 where r is the radius • Example: r = 6 mm • V sphere = 4r3/3 • V = [4 x (6 mm)3]/3 • V = [4 x 216 mm3]/3 • V = [864 mm3]/3 • V = 288 mm3

  16. Measurement • Triangular Pyramid • Square Pyramid

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