Measurement

1
Measurement
2
Introduction

• There are many different ways that measurement is
  used in
• the real world. When you stand on a scale to see
  how
• much you weigh, you are measuring. Here are a
  few fact
• about Mississippi and the Earth using
  measurement
• Woodall Mountain is the highest point in the
  state of Mississippi. This mountain rises 806
  feet above sea level.
• The area of Mississippi is about 125,444 km2.
• The circumference of the Earth is calculated to
  be about 25,000 miles.

3
Length

• To measure customary units in length, use an inch
  ruler for length of 1 foot or less, a yardstick
  for lengths of 3 feet or less, and a tape measure
  for longer lengths.
• To measure metric units of length, use a
  centimeter ruler for lengths up to 30
  centimeters, a meter stick for lengths of 1 meter
  or less, and a tape measure for longer lengths.

4
ExampleWhat is the measure of the long side of
this rectangle to the nearest 1/16 inch?

• Step 1Place the ruler beneath the rectangle.
  Align the 0-mark of the ruler with the left edge
  of the rectangle.
• Step 2Read the mark on the ruler that aligns
  with the right edge of the rectangle.
• The mark is 6 marks after the 3.
• The length is 3 6/16 inches.
• Step 3Write the length in simplest form.
• 3 6/16 3 3/8
• The length of the long side of the rectangle is 3
  3/8 inches.

5
Perimeter

• Perimeter measures the distance around the
  outside of a closed figure.
• To find the perimeter of a polygon, add the
  lengths of all the sides.
• To find the perimeter of a rectangle, you can use
  the following formula P 2l 2w
• To find the perimeter of a regular polygon,
  multiply the length of a side times the number of
  sides.

6
ExampleWhat is the perimeter of this rectangle?

• Use the formula P 2l 2w
• Substitute the length and the width into the
  formula. Then compute.
• P (2 27.5 mm) (2 16.25 mm)
• P 55 mm 32.5 mm 87.5 mm
• The perimeter is 8.5 millimeters.

7
Composite Figure

• A composite figure is a figure composed of two or
  more figures.
• To determine the perimeter of a composite figure,
  measure the distance around the outside of the
  figure.

8
ExampleWhat is the perimeter of the composite
figure?

• 5 cm
  3 cm
• 4 cm
• 
  
• 
  4 cm
• 
  3 cm 5 cm
  
• Find the lengths of the missing sides. Then add
  the side lengths.
• Use the properties of congruent figures to find
  the missing measures.
• The rectangle has a width of 4 cm.
• The left side of the rectangle is 4 cm.
• Add the lengths of the sides.
• 5 cm 3 cm 4 cm 4 cm 5 cm 3 cm 4 cm
  4 cm 32 cm
• The perimeter of the figure is 32 cm.

4 cm
9
Circumference

• Circumference is the distance around the outside
  of a circle.
• The circumference of a circle can be found if you
  know the length of either the radius or the
  diameter.
• The radius is a line segment of the center to any
  point on the circle.
• The diameter is a line segment with any two
  points on the circle that passes through the
  center. The diameter is twice the length of the
  radius.
• If you know the radius of a circle, you can use
  the formula C 2pr to find the circumference.
• If you know the diameter, you can use the formula
  C pd.
• p(pi) is the circumference divided by the
  diameter.
• The exact value of p has never been determined,
  but you can use either 3.14 or 3 1/7 as an
  approximate value.

10
ExampleWhat is the approximate circumference of
a circle with a radius of 7 centimeters? Use
3.14 for p.

• Use the formula for the circumference of a
  circle C 2pr.
• Substitute the value for the variable. Then
  multiply.
• Substitute the value for the variable. Then
  multiply.
• C 2 3.14 7 43.96
• The approximate circumference of the circle is
  43.96 cm.

11
Area

• Area measures the inside region of a closed
  figure.
• Area is measured in square units.
• A square unit is an area equal to that of a
  square whose sides are one unit long.
• For example, a square centimeter (cm²) is an area
  equal to that of a square whose sides are 1 cm
  long.
• To find the area of a rectangle, use the formula
  A lw.

12
ExampleA rectangular playground has a length of
35 yards and width of 25 yards. What is the area
of the playground?

• Use the formula for the area of a rectangle A
  lw.
• A 35 yd 25 yd
• A 875 yd²
• The area of the playground is 875 yd².

13
ExampleLees property is 400 feet long by 200
feet wide. What is the area of Lees property?

• Use the formula for the area of a square A
  s².
• A 400 ft 200 ft
• A 80,000 ft²
• The area of Lees property is 80,000 ft².