Perimeter, Area, and Volume

1
Perimeter, Area, and Volume

• Geometry
• and
• Measurement

2
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
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
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
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
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
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
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
Measurement

• Circle
• Area
• A ?r2, where r radius
• Example r 3 cm
• A circle ?r2
• A ?(3 cm)2
• A 9? cm2

10
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
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
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
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
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
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