PerimeterPerimeterPerimeterPerimeter is the is the

distance all of the way distance all of the way around an object and is around an object and is

find by adding the find by adding the lengths of all of the sides lengths of all of the sides

together.together.

EXAMPLEEXAMPLE

Find the perimeter of a square whose Find the perimeter of a square whose side length is 5 meters.side length is 5 meters.

We know that a square has four sides, We know that a square has four sides, and each is the same length. and each is the same length.

Therefore, to find the perimeter we would add 5 meters four times:

5m + 5m + 5m + 5m =

20m

EXAMPLEEXAMPLE

How much fencing would be needed to How much fencing would be needed to border a yard that is 250 feet long and border a yard that is 250 feet long and 100 feet wide?100 feet wide?

Again, we need to find the perimeter to Again, we need to find the perimeter to solve this problem. In this case, we solve this problem. In this case, we would add 100 ft two times and 250 ft would add 100 ft two times and 250 ft two times because we need to go all of two times because we need to go all of the way around the yard.the way around the yard.

250 ft + 250 ft + 100 ft + 100 ft = 250 ft + 250 ft + 100 ft + 100 ft =

700 ft of fencing700 ft of fencing

EXAMPLEEXAMPLE

Find the perimeter of a triangle that is Find the perimeter of a triangle that is located at the coordinates (5, 6), (2, 2) located at the coordinates (5, 6), (2, 2) and (-2, 5).and (-2, 5).

When you get to an When you get to an

problem like this, problem like this,

always draw it to help always draw it to help

you visualize theyou visualize the

situation.situation.

Cont’dCont’dTo find the perimeter, we will need to find the To find the perimeter, we will need to find the

distance between each of these points distance between each of these points using the distance formula and then add using the distance formula and then add those distances up.those distances up.

The distance formula is:The distance formula is:

1.1. Find the distance between (2, 2) and (5, 6)Find the distance between (2, 2) and (5, 6)

2.2. Find the distance between (5, 6) and (-2, 5)Find the distance between (5, 6) and (-2, 5)

3.3. Find the distance between (2, 2) and (-2, 5)Find the distance between (2, 2) and (-2, 5)

So the perimeter is 5 + 7.1 + 5 = 17.1So the perimeter is 5 + 7.1 + 5 = 17.1

2 2(6 2) (5 2) 5

2 22 1 2 1( ) ( )y y x x

2 2(6 5) (5 2) 50 7.1

2 2(5 2) ( 2 2) 5

What About Circles? What About Circles? ActivityActivity

You will need: You will need: stringstring and and a a rulerruler

Remember, the perimeter is the distance Remember, the perimeter is the distance all of the way around an object. When all of the way around an object. When we are finding the perimeter of a we are finding the perimeter of a circle, we give that a special name. We circle, we give that a special name. We call it the call it the circumferencecircumference..

Take a piece of string and measure its Take a piece of string and measure its length. In our case our string measure length. In our case our string measure 31.4 cm.31.4 cm.

Cont’dCont’d

Take your string and turn it into a circle. Now we Take your string and turn it into a circle. Now we have a circle whose circumference is equal to have a circle whose circumference is equal to the length of the string, in our case 31.4 cm.the length of the string, in our case 31.4 cm.

Now measure the Now measure the diameterdiameter of the of the

circle. circle. DiameterDiameter is the distance is the distance

across the circle, going throughacross the circle, going through

it’s center. Our diameter is 10 cmit’s center. Our diameter is 10 cm

Cont’dCont’d

Take your circumference and divide it by Take your circumference and divide it by the diameter. Here is our equation:the diameter. Here is our equation:

Circumference/diameter = 31.4/10 = 3.14Circumference/diameter = 31.4/10 = 3.14

KEY POINT:KEY POINT: No matter what you had for No matter what you had for your circumference and diameter, when your circumference and diameter, when you divide you should you divide you should alwaysalways get get 3.14!3.14!

Discovering PiDiscovering Pi

This special number, rounded to 3.14, This special number, rounded to 3.14, is called is called

PiPi

(pronounced “pie”) (pronounced “pie”)

and is denoted by the symbol and is denoted by the symbol ππ..