Let's go to the board and just work a couple of problems that involve area. Find the area, and here I have a square.
Each side is 5 inches. So, I want to find the area of this square. The area will be 5(5), or I could write 5²,
either way it's going to be 25 square inches; so, I'll just write inches with a little exponent 2, that means square inches.
Or I could write out square inches, either way. But the surface area, or the area of this square, if each side is 5 inches, the area then is 25 square inches.
Our next problem, we have kind of a geometric figure here. This is 8, this is 8, this is 8 and this is 8. So, I want to find the area of this,
we just draw a little line down right here for myself, inside here, this area, will simply be 8 times 8, which is 64.
Now, over here, this area, is going to be 8 times, this is 8, plus this is another 8 right here, centimeters;
so, I'm going to have the area here, 8 times 8 plus 8, which is 16. So, 8 times 16 for the area of that. Let's see, 8 times 6 is 32, carry the 3,
8, 9, 10, 11. 6 times 8 is 48, what did I say? 32. Okay, 8 times 6 is 48, carry the 4, 8 times 1 is 8 and 4 is 12, 128.
So, I made a little mistake there in multiplication, and my assistant found that real quickly for me. So, 8 times 6 is 48, carry the 4;
8 times 1 is 8 plus 4 is 128. So the area is of the whole figure is the sum of this area plus this area, so I have 64 plus 128, I'll add those, 8 and 4 is 12;
carry the 1, get 9, and 1. So 192 square centimeters for the area of this geometric figure.
The next geometric figure we want to find the area for is called a parallelogram, and I've drawn it over here, it's a parallelogram with a base of 10 feet
and a height of 6 feet. Now, it turns out with all parallelograms, the formula for the area is just the base times the height, and I'll show you why.
Because these two sides are parallel and these two sides are parallel, this length, ten feet, must be the same as this length up here.
So, that must be 10 feet also. Now, to see how we can find the area of this, one way to look at it, is just simply like this.
I'm going to take this little triangle on the end, and move it over here. When I do that, I change my parallelogram into a rectangle,
where this width is 6 feet, because this triangle and this triangle are exactly the same triangle. So, here I have a rectangle with a width of 6,
and a length of 10, and I know from my previous work that to find the formula for the area of a rectangle I simply multiply length times width.
So, I'll write the area as 6 times 10, which is 60, square feet. And you can see that that 60 square feet is exactly the same thing I would get,
if I multiplied this base, 10, times this height, 6. So, all parallelograms work the same way, the formula for the area is the base times height;
and you can always see it by moving the little triangle on one side over to the other side and forming a rectangle.
Now, the next thing we want to do, is find the area of the circle, and we're going to pick up a problem that we started previously about half way through.
We worked this problem before, finding the perimeter of this circle, and now we're going to go, and find its area.
So, let's take a look at this problem, right here. The next thing I want to do, is find the area of this circle, and I'm going to use a different formula.
a is equal to pi, times the square of the radius. So, that will be 3.14 times 4 squared. So, I end up with 3.14 times 16.
3.14 times 16, and I'll just multiply that out, and tell you what I get, 50.24 square inches.
So, that's the area, and I won't actually show you that multiplication, this is, I multiplied it out earlier and this is what I get, 50.24 square inches.
So, that is a circle with a radius of 4 inches, I have a circumference for it, and the units are in inches and in an area the units are in square inches.
So, that's a look at how we find the area of a circle, by multiplying pi times the square of the radius.
Now, you'll notice that some of the problem numbers on the videos you're watching in this chapter will be kind of mixed up,
it won't match some of the things you see on the screen. That's because we're editing some of these video clips together from older clips
that we've done before. So, if the problem numbers are a little off, don't let that stand in your way.
We want to work one more problem involving area, let's take a look at it. I want to find the area, now let's see.
The dimensions here, this 12 inches stands for the distance from here all the way over to here. This is 10 inches, and this down here is 20 inches.
So, since this is 20 inches, this must be 20 inches here. Since this is 10, this must be 10, so that tells me that this little thing right here is going to be 2.
So, let's see, I can find first of all the area of this rectangle right here, it has a length of 10, and a width of 5, so that area,
where that is going to be 5 times 10. And I'll put in my units in a second. Plus, now the area of this, this distance right here must also be 10,
from here to here, because this is 20, so this must be 20, if this is already 10, this must be 10 also.
So, now I have, let's see, 8 inches for this length right here, 10 inches for this distance, so that area will be 8 times 10.
The last thing I have is the area of this little triangle, and from the book I know that the area of a triangle is 1/2 times the base, which is 2,
times the height, which is 8. So, let's see, I end up with 50, that's 5 times 10, plus 80, which is 8 times 10, plus 1/2 times 2 is 1, times 8 is 8.
So, I should end up with 50 plus 80, which is 130, plus 8 is 138 square inches. So, I'll write my units that way on the end.
138 square inches. So, when you see little figures like this, don't be afraid to draw in some vertical lines or horizontal lines to divide it up
into a number of separate little simple figures, find the area of each one of those, add those areas together,
that will be the area of the whole figure.