WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over the area of a parallelogram.
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First let's talk about area.
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An area of a figure is the number of square units it encloses.
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Another way to think of area is how much space it covers.
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Let's say you have to cover your book.
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That is all area because you are covering something.
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It is how much space that you are covering.
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If you have a hole in your jeans and you need to patch it up,
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that is going to be area because it is the space that you are covering.
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This, square units, it means how many 1 unit squares it covers.
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This rectangle here, if I say that there are 8 square units,
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that means each one of these squares, if it has a measure of 1 unit.
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Units can be like centimeters, inches, whatever; this is 1; this is 1.
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The area of this right here is 1 square unit.
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How many square units is in this rectangle?--1, 2, 3, 4, 5, 6, 7, 8.
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The area is 8 square units; it is how many square units it is covering.
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If I say this is 1 inch, then this is 8 inches squared.
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8 square units is 8 inches squared; that is area.
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We know the area of a rectangle is base times height.
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Area equals base times height.
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A rectangle is a type of parallelogram; we learned that in the previous lesson.
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A rectangle is a type of parallelogram; that formula applies to rectangles and to parallelograms.
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Here this is a rectangle.
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If this is the base, this is the height, we just multiply this side with side and we get the area.
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We figure out how much space this is covering.
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For parallelogram, if I maybe let's say I cut this whole part out.
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This is the height; height always has to be perpendicular to the base.
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This is the height; this is the base.
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This whole thing is the base; height, base, perpendicular.
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If I cut this piece out, say I am going to cut this out.
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I take it over to this side; I glue it over here.
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This is all going to be right here; then what do you get?
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This part I cut out; then isn't this part a rectangle?
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All this then becomes a rectangle; this is gone; this was moved over here.
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A parallelogram covers the same amount of space as a rectangle.
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So the formula is still the same.
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Just make sure if you are going to find the area of a parallelogram,
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you have to make sure that the height is perpendicular.
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The height is from here to here; that is the height.
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This right here cannot be the height.
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It is like when you measure how tall you are,
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if you measure your height, you have to be standing up straight.
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You can't be slouching; you can't be leaning over to the side.
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Same thing; the height of this parallelogram is not the side that is leaning over.
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It has to be straight perpendicular; that is the height.
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The first example, we are going to find the area of this rectangle.
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We know it is a rectangle with four congruent sides, meaning four sides are the same.
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That means this is actually a square; a square is a type of rectangle.
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If this is 5, this is also 5.
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The area is base times height which is 5² or 5 times 5.
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We know that is 25; then units, centimeters.
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For area, because we are looking at how much space it covers,
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it is centimeters squared because we are looking at base and height, two dimensions.
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The area of this is 25 centimeters squared.
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Find the area of the parallelogram.
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The first one, this is 9 inches, 7 inches, and 6 inches.
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The area is base times height.
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Again remember the height and the base, they have to be perpendicular.
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If I want to measure how tall the height of this perpendicular, I can't measure thi8s.
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I can't measure it this way.
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I have to make sure I measure it perpendicular, straight up and down.
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The base will be 9; the height is going to be 6.
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The area is 54 inches squared.
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The next one, same thing; this is a parallelogram with four congruent sides.
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We know that this a rhombus; the area is base times height.
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Let's see; what is the base?
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Even though we know that that is 2, that has nothing to do with our base.
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The base is from here to here; that is 10.
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Our height, even though the height is given to you on the outside of it,
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it still measures from top straight down, perpendicular.
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The height is 8; the area becomes 80 meters squared.
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The next example, the base of a parallelogram is 10 inches.
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The height is twice the base; find the area of the parallelogram.
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If I draw a parallelogram, say there is my parallelogram.
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The base is 10 inches; the height is twice the base.
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Make sure you don't label this the height; the height has to be perpendicular.
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You can draw a dotted line like that; that is twice the base.
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Twice means 2 times the base; double the length of the base.
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This is 2 times 10 which is 20.
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The base is 10; it is twice; 2 times bigger, then it is 20 inches.
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Area of this parallelogram is base times height; the base is 10.
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The height is 20; 10 times 20 is 200.
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It is in inches; it is inches squared.
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The final example, find the area of the shaded region; we have two rectangles here.
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This is the big one; here is the smaller one that is inside.
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We are just trying to find the area of just the blue part, the shaded part.
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That means I need to do two things.
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I have to find the area of both rectangles; then I have to do what?
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It is like saying... let's say I have a piece of paper.
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Let's say this big rectangle is the piece of paper.
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If I find the area of that this big rectangle,
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that is going to be the area of that piece of paper, the whole thing.
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But then I cut a rectangle out of that paper; it becomes white.
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How would I figure this out?
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I need to find the area of the big rectangle.
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That is going to be everything.
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If I find the area of the big rectangle, it is going to be this whole thing.
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That is our piece of paper.
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If I cut out another rectangle piece right there like that,
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don't I subtract it?--because it is no longer there.
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This base right here is empty; it is not being covered.
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You have to subtract it; subtract the small rectangle; you are cutting it out.
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That is going to be the area of the shaded.
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Again the whole thing, the area of the big one is going to be 20 times 9.
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The base times the height; 20 times 9.
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That is... 20 times 9; 2 times 9 is 18.
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Then I can just add a 0 at the end of that.
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That is how you multiply numbers.
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If I have a 0 at the end of a number that I am multiplying,
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then I can just put that 0 at the end of my answer.
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It is 20 times 9; you can just do that too; 0 and then 18.
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That is where that 0 comes from; meters squared.
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That is the area of this big one.
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I can't say that is my answer because remember you cut out that little piece.
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This part is not covering anything; it is an open spot.
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To find the area of this rectangle, this is the area of just the first one.
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Let's say that is the first one.
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The area of the second one is 10; the base is 10.
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Times, the height is 3; the area is 30 meters squared.
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This is the part that we cut out.
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I have to subtract it because it was originally covering this much space.
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But then I cut out this much; I have to subtract it.
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My area of the shaded becomes then 150 meters squared.
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That is it for this lesson; thank you for watching Educator.com.