Finding Area

Uploaded by MuchoMath on 12.07.2008

>> Professor Perez: Hey!
This is Professor Perez from Saddleback College.
Today, we're going to find the area of some figures.
But of course, we cannot get started without our student of the semester, and that's Charlie.
I think this is his favorite subject!
Let's see what he's up to!
Hey, Charlie, you ready to go?
We're doing your favorite subject!
It's finding area!
Yeah, he likes these, doesn't he?
All right, Charlie, quit fooling around.
Here we go, right here.
Here's our first figure right here.
Okay, Charlie, here's our figure, that was 5 centimeters, 10 centimeters,
1 centimeter, and that's 6 centimeters.
And those two side lengths are missing.
Now this figure is the same one in the Perimeter Video.
So, to find those missing side lengths, you have to go back
to the Perimeter Video to get a detailed explanation.
For now, we're just going to say that each of them were found to be 4 and 4.
So go back to that Perimeter Video and watch it before you watch this one.
All right, Charlie, here we go.
We have our shape, we're going to find the area.
So let's take our shape and let's center it right here, nice and big for you.
Now we're going to break it up into two separate rectangles.
Now, some people like to take the approach where they build this big rectangle
and then they subtract a littler one from it to do this.
Yeah, that will work fine on this particular figure which is relatively simple.
But we want to learn how to break up these shapes into separate rectangles because later
on in the semester, the figures will get a little bit more complicated and you're going
to separate them into pieces where you'll have a rectangle here,
a semicircle here, and a triangle over here.
So, our goal is to learn how to separate this into rectangles.
So the way I'm going to do this, Charlie, is I'm going to cut this right there.
And I'm going to make two rectangles, this is rectangle one, and that's rectangle two.
Now, the dimensions for rectangle one, it's 5 high and 4 across.
So, I don't need that 4 over there.
The dimensions for rectangle one are 5 by 4.
And for rectangle two, Charlie, I can see that rectangle two is 6 centimeters long
and 1 centimeter in its width, and so we don't need that 10,
that 10 went all the way across, we don't need that.
Now, what I'm going to do, Charlie, is separate these rectangles for you.
So, here we go.
>> Charlie: Oooh!
>> Professor Perez: There they go.
Now, we have two rectangles, and all we've got to do is find the area
of each individual rectangle and then sum them up to get our final answer.
Here we go, Charlie, what's the formula for area for a rectangle?
>> Charlie: Length times width.
>> Professor Perez: Length times width, that's right.
So area one will be length times width, or base times height depending on how you were taught.
And so our dimensions are 4 centimeters by 5 centimeters, okay?
So we'll put 4 centimeters times 5 centimeters.
Remember, by the commutative property, 4 times 5 is the same as 5 times 4
so you can put it in any order you want.
Okay, now, what's 4 times 5, Charlie?
>> Charlie: 20.
>> Professor Perez: 20.
Now don't forget, you have dimensions here.
And we have centimeters times centimeters.
So, some people like to think of it as, okay,
centimeters times centimeters is centimeters with an exponent, a 2.
And that's how it's written.
It's centimeters with a little exponent 2.
But that means centimeters squared.
Dimensions for area are always something squared.
Since our side lengths were given in centimeters, it's centimeters squared.
If our side lengths were given in inches, it would be inches squared.
If your side lengths were in feet, it would be feet squared.
But since we're given centimeters, our dimensions are centimeters squared.
So the area of this rectangle is 20 centimeters squared, okay?
Now, let's go to rectangle two.
Area two is 6 centimeters times 1 centimeter, or 1 centimeter times 6 centimeters.
Okay, what's 6 times 1, Charlie?
>> Charlie: 6.
>> Professor Perez: 6.
And how do you write centimeters times centimeters?
>> Charlie: Centimeters squared.
>> Professor Perez: Centimeters squared, that's right.
And so, to get our total area, we're going to sum up area one and area two.
So, area one plus area two is 20 plus 6 centimeters squared,
which gives up 26 centimeters squared and there's our answer there.
26 centimeters squared.
Very nice there, Charlie.
All right.
Now let's go to a more complicated problem, no don't get scared.
Here it comes, Charlie.
There you go!
>> Charlie: Oh...
>> Professor Perez: Oh, you like that one too, huh?
All right.
Don't worry, we'll just work at it and it will be really easy.
Watch. We're going to break it up into rectangles.
Now notice the two missing side lengths.
And again, this figure was used in the Perimeter Video, so to find those missing lengths,
side lengths, go back to the Perimeter Video.
But this one was found to be 5 inches and that one was found to be 14 inches.
Notice our dimensions are given in inches so since we're finding area,
our dimensions will be inches squared.
All right.
So, let's center this for you Charlie.
Let's put it over here so you can see it.
Really big.
And we're going to break it up into pieces.
Watch. We're going to make a cut up here, and a cut down here.
And I'm going to call that top rectangle one,
this one down here two, and this one over here three.
Very nice there.
Okay. Now, my top rectangle, Charlie, how long is it?
>> Charlie: 17.
>> Professor Perez: 17 and how wide is it?
>> Charlie: 4.
>> Professor Perez: 4, so that 14 I don't need right there.
Rectangle one.
Length 17, width 4 inches.
Now, rectangle two over here.
How tall is rectangle two, Charlie?
>> Charlie: 5.
>> Professor Perez: It's that 5 inches.
Now that 11 inches runs all the way up and down, we don't need that.
But we do have to find out how wide that is.
And to find that width, you should go back to the Perimeter Video, right?
If you're having problems finding it, it is 3 inches.
Well, from here, notice the whole bottom length here is 10, and that one 7,
so that length right there should be 3.
That's 3 inches, that's how we found it in the Perimeter Video.
And so that takes care of the dimensions for rectangle two.
Now rectangle three.
How long is rectangle three, Charlie?
>> Charlie: 10.
>> Professor Perez: 10, and it's width is...2, so that 7 we don't need.
It's the way I broke it up.
And so we have three separate rectangles, Charlie, now hold on.
We're going to separate again.
Here we go.
>> Charlie: Aaahhh!!
>> Professor Perez: Quit fooling around over there, Charlie!
This is serious stuff here!
All right.
Okay, let's find the area of each individual rectangle now.
Remember, what's the formula for area, Charlie?
>> Charlie: Length times width.
>> Professor Perez: Length times width.
So for rectangle one, the area is 17 inches times 4 inches.
Now, 17 times 4, remember, we don't use calculators in the first half of this class
so you better not be using a calculator.
You don't want to become one of those calculator kids, do you?
No. We want to not use a calculator for the first half.
The second half when we get to the more complicated we will be using a calculator.
Now you can use a calculator now to check your answer, but, let's talk about 17 times 4.
Let's try and visualize this and try some Kung-Fu, watch.
Okay, here we go.
Visualize in our mind.
We have 17 times 4, right?
That's what we have there, 17 times 4.
Now think of the 17 in expanded form, meaning 17 is 10 plus 7.
And we're multiplying 10 plus 7 times 4.
So, each the 10 and the 7 have to be distributed to the 4.
Right? It's the distributive property.
So what's 10 times 4, Charlie?
>> Charlie: 40.
>> Professor Perez: 40.
What's 7 times 4?
>> Charlie: 28.
>> Professor Perez: 28.
And what's 40 plus 28?
>> Charlie: 68.
>> Professor Perez: 68.
That is 17 times 4.
So, that is one approach.
Okay, rectangle two, it's are is just 3 inches times 5 inches, or 5 inches times 3 inches
by the commutative property for multiplication.
And we get 15 inches squared.
Don't forget your dimensions.
Now, rectangle three, Charlie.
That's 10 inches times 2 inches which should be easy.
That's what?
>> Charlie: 20.
>> Professor Perez: 20 inches squared.
And now, to find the total area, we can just sum up these individual areas.
So our area total, we have to take 68 plus 15 plus 20.
And you can add those in any order.
Well, one approach would be 15 plus 20 is what, Charlie?
15 plus 20?
>> Charlie: 35.
>> Professor Perez: 35 inches squared, and adding that to 68.
So, think about this.
68 plus 35.
Well, 60 and 30 is 90, and 8 and 5 is 13, and so 90 and 13 is 103.
Again, that's one approach.
Or you can just write them in a column and just do it, right?
Add all the numbers up, get your answer.
It should be 103 inches squared.
Don't forget, it's area, so the dimensions, it has 2 dimensions, it's 103 inches squared.
Anyway, it's a tough problem there.
Anyway, we got through it.
Phew! We'll see you all again soon!