Finding the Perimeter:
Topic Index | Grade 5 Math | Intermediate Test Prep | StudyZone


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.

Let's Practice!