Perimeter and Area

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Perimeter and Area

• by Scott Alan Blanchard
• November 3, 2013

After completing this presentation, you will
understand what is and be able to find the
perimeter and area of a rectangle, square and/or
triangle.
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Where Do YOU need to go?

• Perimeter
• Area, defined
• Area of Squares and Rectangles
• Area of TRIANGLES
• All Done!! Feeling Good!

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Perimeter

• Perimeter is a word used to describe the
  distance around a figure.

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Perimeter

• When we are talking about perimeter we are
  talking about shapes that have non-curved lines.
  So we are talking about triangles, rectangles,
  squares, etc.

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• Heres a square and lets just say that each side
  has a length of 5 cm.
• A B
• D C

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• In other words, line segment AB is 5cm, line
  segment BC is 5 cm, line segment CD is 5 cm, and
  line segment DA is 5 cm.
• A B
• D C

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• To find its perimeter, we would just add up the
  measurement of each of its side.
• So 5 5 5 5 20 cm.
• A B
• D C

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• And heres a rectangle say its a football
  field, with a length of 100 yards and width of
  50.
• 100 yards
• 50 yards 50 yards
• 100 yards

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• To find its perimeter, think of walking all the
  way around the field
• 100 yards
• 50 yards 50 yards
• 100 yards

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• you could start at one corner and walk 100 yards
  down and then 50 yards up, then 100 yards back
  and 50 yards back to where you started.
  
• 
  100 yards
• 50 yards 50 yards
• 100 yards

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• That would be a perimeter of 300 yards!!
• 
  100 yards
• 50 yards 50 yards
• 100 yards

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• Think youve got the hang of perimeter?
• Its really not too hard. Its the same for all
  non-curved geometric shapes.
• Lets try a TRY-ANGLE now, O.K.?

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• Lets give this triangle the following sides
• AB 15 cm,
• BC 22 cm, and
• AC 17 cm.
• See
• B
• A C

22 cm
15 cm
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17 cm
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• In your head, figure out what you think the
  perimeter would be for this triangle. Keep that
  number in your head and then hit next.
• AB 15 cm,
• BC 22 cm, and
• AC 17 cm.
• B
• A C

22 cm
15 cm
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17 cm
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• To find the perimeter of a triangle, simply add
  the sides together.
• 15
• 22
• 17
• 54 cm.
• Is that what you got? I hope so!
• B
• A C

22 cm
15 cm
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17 cm
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Another way to think of perimeter, is to think of
it as if you were an ant and you had to walk all
the way around the object. How far would you
have to walk?
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Just like when you walk somewhere, you ask how
far away it is, perimeter, is pretty similar to
that.
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• Can you think of a rectangle, square or triangle
  you are looking at right now?? There is probably
  more than one to see in the room you are in right
  now.

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• The computer screen is probably in the shape of
  a rectangle.
• Right?

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• Lets find its perimeter.
• Are you ready?

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Lets say this is your computer!!Pretty cool,
huh?!?

• Lets give it a 15 wide and 10 high monitor.
• 
  So what would its perimeter
  be?

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• We gave YOUR laptop a 15 wide and 10 high
  monitor.
• 
  So what would its perimeter
  be?
• Remember 50 centimeters
• now that 45 inches
• perimeter 50 inches
• equals 60 inches
• the distance
• around

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• ??ps. You are not using the right measurement.
• TRY AGAIN!!

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• 15 10 15 10 ? 45
• TRY AGAIN

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• What?!?!?!?
• My dog can count better than that!!
• 15
• 10
• 15
• 10
• Now YOU are trying to tell me that this is 60????
  Ha, ha, ha, ha,thats good!!
• TRY AGAIN

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• GREAT!!
• Now try this one..
• Heres a square CDEF. Each side has a length of
  7 mm. What is its perimeter?
• C D
• E F

• 24 cm
• 27 mm
• 28 mm
• 29 cm

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Auggh!!

• Be sure to check your adding and your units of
  measurement!!

Try Again, Please
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GREAT!! Now, lets try this isosceles triangle.
Isosceles triangles have two sides that have
the same measure, and one that is longer or
shorter than the others.
Q R S

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In this triangle, QRS, QR and QS will have
lengths of 10 inches and RS will have a length
of 15inches. What is the perimeter of triangle
QRS?
Q R S

• 35 centimeters
• 25 inches
• 35 inches

10 inches
10 inches
15 inches
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• Come on, NOW, dont guess!! THINK!!
• Check your addition and units!

TRY AGAIN
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• GREAT Job!!
• You remembered to add up the measurements of all
  the sides to get the perimeter!!
  Congratulations!!
• YOU are a Powerful Perimeter-er!!

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Congratulations!! YOU are now a Perfect
Perimeter Person!!
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Perimeter
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• AREA

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• The official definition of area, as it pertains
  to mathematics, from Merriam-Webster is the
  surface included within a set of lines
  specifically the number of unit squares equal
  in measure to the surface.
• Pretty boring, huh? On its own it is, but well
  get into what all that means in this exploration.
  
• Are you ready?
• Lets go..

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• Area is more easily defined as a measure of the
  space inside a closed, two-dimensional figure.

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• By being closed it means that the shape comes
  to end where it started. You stop drawing a
  circle where you start it.

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• By being two-dimensional, the figures we will be
  dealing with are basically flatdrawn on paper.
  

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• In essence, the area of a shape is how many
  square units fit inside of that shape.

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• In the shapes below, if you counted how many
  squares were in each, you would know its area in
  square units.

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• You might be saying, Hey, wait a minute!! The
  triangle and circle have parts of squares in
  them!
• Well, actually, you are partly correct.

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• In mathematics, everything ultimately works out
  just right. The little bits of leftover
  squares combine and make squares. And we get a
  final answer, as the game show says.

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• With this rectangle we can squint real hard and
  count 20 full squares from side to side and 24
  full squares from top to bottom. But on the very
  top and on the left side, it is obvious that we
  have anything but full squares.

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• What I was talking about earlier is that those
  will get combined and get taken care of.

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• When finding perimeter, we just needed to count
  the distance around. For area, we count the
  amount inside. So we are going to count the
  number of squares (or square units) inside.

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• The square units has to do with whether we are
  dealing with inches, millimeters, centimeters,
  kilometers, etc. etc Whatever measure of units
  we are measuring our flat 2 dimensional object
  in.

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• I said we were going to count the square units
  inside the object. Well, not really, because we
  are going to learn a rule for area multiply the
  length times the base.the number from side to
  side times the number from top to bottom.

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• The rule for finding area of a square or
  rectangle is
• A H X W
• H
• W

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• I said earlier that in this rectangle there are
  20 squares from side to side and 24 from top to
  bottom. So now, according to that rule, we
  multiply 20 and 24 and get 480. Right?
• 24H
• W20

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• Wrong!!

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• Wrong!?
• You say, How come?!? 20 X 24 480.
• Well, yes, it does equal 480,sort of. You forgot
  your units!

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• You say, You didnt give us any units!
• Well, then your answer is stated in just units,
  then. But when we deal with area, our units are
  squared, since we are counting the number of
  little squares.

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• So the correct answer is 480 square units or 480
  units squared, or you may even see it written
  this way 480 units2.

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• And if you wanted to take the time to, you could
  count and find there are 480 small squares in
  there. (you might have to put parts of squares
  together to make whole squares)

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• The basic formula for area for a square or
  rectangle is
• Area Base X Height
• For example lets say that the base of this
  rectangle is 50 mm, and its height is 18 mm.
• Then its area would be 50 mm X 18 mm 900 mm2.

1 8 m m
50 mm
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• Here, lets say that the base of this rectangle
  is 70 mm, and its height is 20 mm.
• Then its area would be 70 mm X 20 mm 1400
  mm2.

2 0 m m
70 mm
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Why dont you try?
100 yards
50 yards

• Whats the area?
• 5000 yards2
• 5000 yards
• 50000 yards2

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KaBooooooooooooooom!!! Youve just exploded on
that one!! Watch your arithmetic!! And dont
forget to check your units of measurement.
Remember area is equal to B X H.
Now, Go Back and Watch Out!!
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• Why dont you try a word problem?
• What would the area be for a rectangle with a
  base of 7 mm and height of 2 mm?
• 9 mm
• 14cm2
• 14mm2

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• Think! Think ! Think!

Try Again
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• SUPER!!
• Heres another one
• A rectangle with a base of 12 cm and height of 5
  cm would have an area of?
• 50 cm2
• 60 cm2
• 60 cm

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• Auggh!!!
• Be careful. Be VERY, VERY careful!
• Try again, please!

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• Waaaay to GOOO!!
• Give a try at this one now!
• What would the area of this rectangle be?

5 feet

• 100 feet2
• 100 feet
• 90 feet2

20 feet
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• Please keep trying. I just know YOU can do
  it!!
• Area Base X Height (in units squared)

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• Super Job!!
• Remember the formula for the area of a rectangle
  is
• Base X Height

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• We would find the area for a square the same way,
  because really a square is a rectangle.
• (But YOU already knew that!!)
• Right????

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GREAT!! Now, whats the area for this
square? remember all sides have equal lengths
on squares

• 47 cm2
• 47 mm2
• 49 cm2
• 49 mm2

7 mm
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Remember the area for a square is found by
multiplying the length of a side by itself again.
And also, be sure you are using the right units
in your answer.
Please, Try Again
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Thats Right!! Terrific Theres no fooling
YOU, now is there?!
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Okay, now this one is REAL tricky, but I will
give you a B-I-G hint. I want to see IF you can
do it. Ready to try? Just for fun? If you want,
you can skip it by clicking THIS or click
NEXT for the Challenge. I KNOW YOU CAN DO IT!!
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You will have to find the area of the square
AND the rectangle and then add them together.
Okay? Lets go-gt
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• Okay!!
• Whats the area?
• 5cm
• 5cm
• 10cm

• 250cm2
• 500cm2
• 75cm2

Remember squares have the same measure for ALL
four sides!!
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• Come on, now, I know you can do it!!

Try Again
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You didnt do the challenge, and thats okay!!
But YOU are to be commended, anyway. May the
Squares be with YOU!!
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Area Award
On Squares and Rectangles
Presented to YOU on Sunday, November 03, 2013 at
132016
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• Area of
• Triangles

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• Now, were going to learn about how to find the
  area of a triangle. It is a little different
  than finding the area of a square or rectangle.

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• For perimeter it was pretty easyjust add up all
  of the lengths of the sides.
• It didnt matter. Rectangle, square or triangle.
• But what now, for area??

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• Believe it or not, a triangle is ½ of a square or
  rectangle.
• So its really not that hard, as long as you
  remember how to find the area of a square or
  rectangle.

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• Look at this rectangle below
• What would happen if we cut it diagonally?

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• Wed end up with TWO triangles!!
• The same would happen with a square.

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Here are some squares with diagonals to make
triangles
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• Since we have just seen that a triangle is ½ the
  size of a rectangle or square, what do you think
  is the way to find the area of a triangle??

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• Did you come up with something like this?
• ½ (Area of Rectangle)
• ?or?
• ½ (Area of Square)
• If so, GOOD for YOU!!

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• So, the formula would be,
• Area of a Triangle ½ X BXH

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• It looks like this
• ½(BXH)

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• If the height were ten, and the length were
  twelve of this triangle then its area would be ½
  of 10 X 12.

10
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• or ½ of 120.
• ½ of 120 is. 60.
• So in this example, the area would be 60.
• 60 units squared.

10
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• Lets try some out now. Okay?!?
• Remember the Area of a triangle is found by
  taking ½ of the product of the base and height!
• 12 inches
• 12 inches

• Would the Area be
• 144inches2
• 71 inches2
• 72 inches2

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• Auggh!!
• Dont forget the formula for the Area of a
  Triangle is ½ (B X H)!!

Go back, and Try Again
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• Oh, soooo close!!
• Try again!

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• W?W!!
• Great Job!! Thats right!! ½ of 12 inches X 12
  inches is 72 inches2! Keep it up.

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One more triangle one, I want you to TRY your
ANGLE at
30 inches
10 inches
20 inches
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• What would the AREA be?
• 150 inches2
• 100 inches2
• 160 inches2
• 300 inches2

30 inches
10 inches
20 inches
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Uh-OH!! Are you falling asleep or are you just
not using your brain on this one??
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• Heres another one.
• Try-- your angle --angle at this one!
• Whats the area?

10 inches
10 inches
50 inches2 100 inches2

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Yahoo!!

• Ride em cowboy!!

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• Please try again.
• Your answer is
• INCORRECT!!

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Area Award
On Triangles
Presented to YOU on Sunday, November 03, 2013 at
12016 PM
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• Congratulations!!
• YOU feel confident on the topics of perimeter and
  area and this review is not necessary for you at
  this time.
• Good job for you.
• Come see your teacher for further instructions on
  what to do now