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 triangle.
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The formula for the area of a triangle is base times height divided by 2 or 1/2 base times height.
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Here we have a parallelogram.
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We know that area of a parallelogram is base times height.
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Here is a rectangle; the area of this is base times height.
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If I take this parallelogram and I cut it in half, let's say I cut it this way.
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Then I have two equal halves; I then have a triangle.
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One of these triangles would be the whole thing, the whole parallelogram, cut into half.
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This triangle is base times height divided by 2 because I cut it in half.
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Same thing here.
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If I take this rectangle and I cut it in half, I am going to get the triangle.
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That is why the formula for the area is the base times the height divided by 2.
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Because it is cut in half; base times height, cut in half.
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Here are a couple of triangles; we are going to find the area.
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Again remember area is how much space it is covering.
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We are going to see how much space this triangle is covering.
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The area of this triangle has a formula of 1/2 base times height or base times height divided by 2.
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The base we know is 8; remember base times height.
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It is still the same as the previous lesson when we talked about parallelograms.
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The base and the height have to still be perpendicular.
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When we talk about height, we are talking about the perpendicular height from the highest point to the lowest point.
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It has to be perpendicular; they have to be perpendicular to each other.
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The base is 8; the height is not this side, this side right here.
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It has to be this height; that is 6 inches.
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It is all of that divided by 2.
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8 times 6 is 48; divided by 2.
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This looks like a fraction; but it is also divide.
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48 divided by 2 is 24; our units is in inches; it is inches squared.
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Because it is area, any time you are talking about area, it is always units squared.
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That is the area of this triangle here.
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The next one, area equals the base times the height divided by 2.
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This looks like half of our rectangle we drew.
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That rectangle; it is half of that.
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Base times the height; the base is 5; the height is 10.
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We know that is 10 because it is perpendicular.
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But because we are only looking at half of it, the triangle part, we are going to divide that by 2.
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Area equals 50 divided by 2; 50 in half is 25; centimeters squared.
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Next, find the area of the figure.
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There is no formula to figure out the area of this whole thing in one formula.
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We have to break this up into two parts.
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We know the area of a triangle.
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We know the formula for the area of this rectangle.
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If I put it together, I am going to add the area of this triangle to the area of this rectangle.
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First the area of the triangle.
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I am going to do a triangle plus a rectangle is going to equal...
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All this plus all that is going to equal triangle with that.
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Area of the triangle, triangle first, is 1/2 base times height or base times height divided by 2.
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The base is 6 right here.
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Even though the base is not the one on the bottom,
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this has to be the base because the height and the base have to be perpendicular.
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If you want, you can just redraw this triangle so that this becomes the base like that.
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If this is 6, this side is this side right here.
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Then that is the triangle; this can be 8.
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But just because it is moved, it is rotated where this is right here, it doesn't change the area.
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Base is 6; the height is 8 meters; divided by 2.
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6 times 8 is 48; divided by 2; half of 48 is 24.
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That is meters squared.
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For the rectangle... because this is only the area of this.
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To find the area of the rectangle, it is just base times the height and not divided by 2.
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The base is 10; the height is 6; they are perpendicular; that is fine.
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This is 60 meters squared; remember what you have to do.
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Take the area of the triangle; add it to the area of the rectangle.
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This is the rectangle.
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It is going to be 24 meters squared plus 60 meters squared.
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Together it is going to be 84 meters squared.
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That is the area of this figure right here.
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For this one, we are going to find the area of the shaded region.
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This is different than the previous one because we had
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two shapes that were put together to make up a figure.
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This is different; this is overlapping.
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Here we are just finding only the area of this right here, all this blue.
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In this case, let's say we have a paper.
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This blue, this whole rectangle here, let's say that is our piece of paper.
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We have a piece of paper that is going to be blue like that.
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We are going to take scissors and we are going to cut out a piece of it; that triangle piece.
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Don't you remove some of the area?--you are uncovering some of the area.
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You have to subtract the triangle there; the area of this minus the triangle.
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That is going to give you that whole thing, cut out the triangle, all of this.
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The previous one we had to add because they were put together.
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But this one, we are going to subtract.
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The area of this rectangle first; a rectangle.
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We know that the formula for the area of a rectangle is base times height.
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The base is 20; the height is 10.
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That is going to be 200 inches squared.
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Then we have to find the area of this triangle because how much space is the triangle using up?
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Because that is how much we have to take away.
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The triangle, area is a base times height divided by 2; the base is 5.
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Again even though this is not the bottom, that is not the base,
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we can still call that the base as long as the base and the height are perpendicular.
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5; and then the height is 6; over 2.
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5 times 6 is 30; divided by 2 is 15; inches squared.
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We have the area of the rectangle and the area of the triangle.
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Let's take the area of a rectangle and subtract, take away
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the area of the triangle to see what is left in blue.
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It is going to be 200 inches squared minus 15 inches squared.
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If you do 200 minus 15, you are going to get 185 left.
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185 inches squared, this will be the area of the shaded region.
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That is it for this lesson; thank you for watching Educator.com.