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Lesson 3: Area of composite figures

Area of composite shapes

We can sometimes calculate the area of a complex shape by dividing it into smaller, more manageable parts. In this example, we can determine the area of two triangles, a rectangle, and a trapezoid, and then add up the areas of the four shapes to get the total area. Created by Sal Khan.

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• Can't you just think of the bottom part as a trapezoid? You can add 6.5 and 3.5 and divide by 2 and multiply that by 9 to get the bottom part. That would save you the hassle of finding the triangle's and the rectangle's area.
• There can be many ways to do composite figures, and your way is just as valid since you divide it into known shapes especially since the area of trapezoids is the first in this string of videos. For fun, I might start with a large 10 by 9 rectangle and take away the three triangles that are cut off from the corner 90 - 3.5 - 13.5 - 12.25 = 60.75.
• What if the shape has a half circle in it?
• Then use the circle formula and divide it by 2.
• I don't understand how to do this can someone explain?!
-\'_'/-
• So what he's saying is that you need to break up the shape to make it easy to divide
• "Say when I grow up, what is this useful for?"
• geometry is useful for architecture, design,renovation, building, art, and sometimes just daily activities. This information will also be helpful if you end up needing or wanting to help someone else that has curriculum revolving around this subject. There many uses for geometry in life.
• can some one explain i'm not giving up but i want to can any one help. Thanks.
• So to find the area of an oddly shaped figure that you don't have a formula for, you split it into lots of smaller figures that you already know how to find the area of. Then you add them all together to find the total area of the original larger figure. Does that make sense? Let me know if there's anything you still don't understand.
• Is the label that important? (square units)
• It helps you know which is which. For example, 25m is a line, but 25m2 is a shape.
• I am sooooo confused about why he did 1 half times 7
• Actually, he meant 1/2*7. That is the same as dividing something by two.
• It's pretty easy. Just transform the shape into squares and rectangles by drawing lines, calculate their area, and add it all up. Easy!
• It depends on who you are and how you learn... Some people may not learn as quickly as you because what language they speak or their environment or their teacher so it may be easy for you because all those thing are good for you
• im brainig so hard my think hurts.
• am i slow, or did this video make no sense at all
• Here is the concept of how to find the area of a composite shape.

1. Divide the shape into simpler shapes such as rectangles, triangles, etc.

2. Find the measurements of each simpler shape. Sometimes you might need to add or subtract to find these measurements.

3. Use these measurements to find the area of each simpler shape. Remember that area is base times height for a rectangle, and 1/2 times base times height for a triangle.

4. Add up the areas of these simpler shapes.

Have a blessed, wonderful day!

Video transcript

- [Instructor] So we have the strange-looking shape here, and then were given some of its dimensions. We know that this side right over here has a length of 3.5, this side over here is 6.5, then we know from here to here is two, and then from here to here is seven, and then they're giving us this dimension right over here is 3.5. And so given that, let's see if we can find the area of this entire figure. And I encourage you to pause the video right now and try this on your own. So I assume you've given a go at it and there might be a few things that jump out at you immediately. The first thing is that they have these two triangles up here and they give us all of the dimensions for 'em, or at least they give us the base and the height for it, which is enough to figure out the area. If I had a triangle or if I had a rectangle that was 2 X 3.5 or two wide, two units wide and 3.5 units high. If had a rectangle like that, we know that it would have an area of 2 X 3.5. Now a triangle is just going to be, or especially a triangle like this, a right triangle is just gonna be half of a rectangle like this. We just care about half of its area. So this area is going to be 1/2 X 2 X 3.5. And 1/2 X 2 = 1, 1 X 3.5 is 3.5 square units. So the area of that part is going to be 3.5 square units. Now let's think about the area of this triangle right over here. Well, once again, we have its height as 3.5, its base is seven. So its area is going to be 1/2 X 7 X 3.5. 1/2 X 7 is 3.5 X 3.5, so this part is 3.5, and then I'm gonna multiply that times 3.5 again. So let's figure out what that product is equal to. So 3.5 X 3.5. 5 X 5 is 25. 3 X 5 is 15 + 2 is 17. Let's cross that out, move one place over to the left. 3 X 5 is 15. 3 X 3 is 9 + 1 is 10. So that gets us to 5 + 0 is five, 7 + 5 is 12. Carry the one, 1 + 1 is two, and we have a one. And we have two digits to the right of the decimal. One, two, so we're gonna have two digits to the right of the decimal in the answer. So the area here is 12.25 square units. Now this region might seem a little bit more maybe, maybe a little bit more difficult because it's kind of a, it's this weird trapezoid-looking thing. But one thing that might pop out at you is that you can divide it very easily into a rectangle and a triangle. And we can actually figure out the dimensions that we need to figure out the areas of each of these. We know what the width of this rectangle is, right? Or the length of this rectangle, whatever you want to call it. It's going to be two units plus seven units. So this is going to be nine. We know that this distance is 3.5. So if this distance right over here is 3.5, then this distance down here has to add up with 3.5 to 6.5. So this must be three. So now we can actually figure out the area. So the area of this rectangle is just going to be its height times its length, or 9 X 3.5. 9 X 3.5. And one way you could do it, we could even try to do this in our head. This is gonna be 9 X 3 + 9 X 0.5. So 9 X 3 is 27. 9 X 0.5, that's just half of nine, so it's gonna be 4.5. 27 + 4 would get us to 31. So that's going to be equal to 31.5. Or you could multiply it out like this if you like. But the area of this region is 31.5. And then the area of this triangle right over here, it's gonna be 9 X 3 X 1/2, we're looking at a triangle. 9 X 3 is 27, 27 X 1/2 is 13.5. And so to find the area of the entire thing, we just have to sum up these areas. So we have 31.5, 31.5 + 13.5, 13.5, plus 12.25, 12.25, plus 3.5, plus 3.5 here. So we just have a five here in the hundredths. That's the only one. 5 + 5 is 10 + 7 is 17. 1 + 1 is 2 + 3 is 5 + 2 is 7 + 3 is 10. 1 + 3 is 4 + 1 is 5 + 1 is six. So we get a total area for this figure of 60.75 square units.