Objective:
Measuring and Calculating
In this lesson you will measure directly and indirectly
and use measurements to describe and compare objects.
You will also demonstrate an understanding of the concept
of rate.
If you need to check a word's definition, please go to the glossary by clicking the Vocabulary button
-
Attribute
-
Area
-
Perimeter
-
Volume
- Circumference
- Dimension
- Rate
| To find the perimeter of a polygon or geometric figure,
you find the distance around it. You will add the lengths
of all sides to arrive at the perimeter. When you find
perimeter, you are working with only one dimension
as you measure around the figure. Since you are only
measuring and adding the lengths around the figure,
the units are labeled as one dimension, usually just
cm, ft, yd, mi, or others. The units are NOT squared
or cubed when finding perimeter because you are working
with one dimension. |
Circumference of a Circle
|
Circumference of a circle is the "perimeter"
or distance around the given circle. To find
the circumference of a circle you multiply the
diameter of the circle times pi. Pi is often
represented as 3.14 or 22/7. One formula for
finding the circumference of a circle is C =
x d or C =
d where C is the circumference and d is the
diameter of the circle. Since the diameter of
a circle is actually two times the radius, which
is half the diameter measurement you could use
another formula which is C = 2 x
x r where r is the length of the radius of the
circle. Since the circumference of a circle
is one dimensional, just finding the length
around the circle, the units are labeled to
the first power or just the units that you are
working with.
For example:
Find the circumference of a circle with a
diameter of 14 inches. Use 22/7 for pi.
C = x d
C = 22/7 x 14
C = 308/7
C = 44 in.
|
To find the area of a rectangle,
use the formula, L x W, where L is
the length of the rectangle and W is
the width of the rectangle. When finding
the area of a rectangle, your results
will be in the units of measurement
squared. The reason the units are labeled
squared is because you are working
with only two dimensions when working
with area, length and width. A =
lw
For example:
Find the area of a rectangle 20 feet
long and 12 feet wide.
A = l x w
A = 20 x 12
A = 240 feet2 or
squared feet
|
To find the area of a triangle,
you use the formula, 1/2 x
b x h, where b represents the
base of the triangle and where
h represents the height of
the triangle. When finding
the area of a triangle, your
results will be in the units
of measurement squared. The
reason the units are labeled
squared is because you are
working with only two dimensions
when working with area, length
and width. A = 1/2 bh
For example:
Find the area of a triangle
with a base of 10.2 feet and
a height of 3.5 feet.
A = 1/2 bh
A = 1/2 (10.2)(3.5)
A = 35.7/2
A = 17.85 feet2or squared
feet
|
One way to find
the volume of a rectangle
is to multiply the
dimensions, the length,
the width, and the
height of the rectangle.
Since we find volume
use the rectangles
three dimensions, the
answer is in units
cubed. You use the
following formula: V
= lwh
For example:
Find the volume of
a rectangle with the
dimensions of 13.5
cm in height, 21 cm
long, and a width of
6.2 cm.
V = lwh
V = 21 x 6.2 x 13.5
V = 130.2 x 13.5
V = 1757.7 cm3 or cubic
cm
|
|
Rate is the quotient
of two quantities with different units. A quantity
whose unit contains the word "per"
or "for each". For example, 35 miles
per hour or 28.5 students per
classroom. You use a slash to show "per".
For example, 35 miles per hour is written as
35 mi/hr and 28.5 students/class.
The rate formula looks like this:
(a
unit1)
x (b
unit2/unit1)
= ab unit2
An example
would be:
Wendy bought
5 cans of split
pea soup at
$1.65 per can.
What is the
total?
5 cans x 1.65
dollars/can
= 5(1.65) dollars
= $8.25
|
| As
you work
with
measurement,
always
be sure
to determine
what
units
are in
your
answer
and then
label
your
answer
such.
For example,
don't
say that
the area
of the
rectangle
is 20.
You want
to be
sure
to include
the units
of measure
as well.
So the
area
of the
rectangle
would
be 20
squared
feet.
Remember
if you
are finding
area,
the units
are squared
and if
you are
finding
volume,
the units
are cubed. |
Example
1 >>
|
