Perimeter
The distance around a
polygon is called the perimeter. Although there are shortcuts
which can be used to find perimeter, the basic process involves
adding all of the lengths of
all of the sides together.
The word "all" has been highlighted
because, even though this is a fairly easy process, the one mistake
many students make is forgetting to add all of the lengths.
Make sure that you include all
of the sides!!
6ft.
+ 3ft.
+ 6ft.
+ 3ft.
= 18ft.
The perimeter is 18 ft. |
Let's start with
an easy example.
|
A new playground is
being built in the neighborhood. It is to be in the
shape of a pentagon. If each of the sides is 45 feet
in length, how many feet of fencing is needed to totally
enclose the area? |
 |
Wait a minute, I
thought this was supposed to be a "perimeter" problem!
Ohhhhh...! I see what's going on, since the fence is going
to go all the way around the playground, when we find out the
number of feet of fencing, we are also finding the
"perimeter"
of the shape!
Pretty sneaky!
Since a pentagon has 5 sides,
all we have to do is add
45 to itself 5 times:
45 + 45 + 45 + 45 + 45 =
or....5(45) =
Both of these processes will work...
In either case the answer is 225 feet.
We use a capital "P" to represent perimeter,
P = 225', they will need 225' of fencing!
|
Let's get a
little more complicated.
|
First, find the value of
"A" and "B" and then find the perimeter of this shape. |
First to find the length of "A" we need to see that if we add the
length of "A" to 19 it would be the same total length as the other
side of the shape (32")
In other words,
"A" + 19 = 32
Solving for "A":
"A" = 13!
Repeat the process for "B"
"B" + 25 = 56
"B" = 31
Now that we have all the
pieces, finding the perimeter is easy!
P = 32 + 56 + 19 + (31) + (13) +25
P = 176"
|
One more....
|
In this
problem all we have to do is make sure that we include only the
sides that actually make up the boundary of this weird shape.
One suggestion is to take your pencil and cross out each side as
it is counted. Whatever method you use, just make sure to
include all of them, but remember the note in the box above, the
sides that are connected are not a part
of the perimeter!
Did you come up with 18 sides??
I hope so...
Since all of the sides are 7.2 cm., all we have
to do is multiply:
P = 18(7.2)
P = 129.6 cm. |
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