Transcript Measurement Introduction There are many different ways that measurement is used in the real world.

Measurement
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.
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.
Example—What is the measure of the long
side of this rectangle to the nearest 1/16
inch?
• Step 1—Place the ruler beneath the rectangle. Align the 0-mark of
the ruler with the left edge of the rectangle.
• Step 2—Read 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 3—Write 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.
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.
Example—What 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.
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.
Example—What is the perimeter of
the composite figure?
5 cm
3 cm
4 cm
4 cm
3 cm
4 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.
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 =
2πr to find the circumference.
• If you know the diameter, you can use the formula C = πd.
• π(pi) is the circumference divided by the diameter.
• The exact value of π has never been determined, but you can
use either 3.14 or 3 1/7 as an approximate value.
Example—What is the approximate circumference
of a circle with a radius of 7 centimeters? Use
3.14 for π.
• Use the formula for the circumference of a
circle: C = 2πr.
• 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.
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.
Example—A 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.
Example—Lee’s property is 400 feet long by 200
feet wide. What is the area of Lee’s property?
• Use the formula for the area of a square:
A = s².
– A = 400 ft • 200 ft
– A = 80,000 ft²
• The area of Lee’s property is 80,000 ft².