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So that would give us the area of a figure that looked like-- let me do it in this pink color. A width of 4 would look something like this. And so this, by definition, is a trapezoid. So we could do any of these. So you multiply each of the bases times the height and then take the average. Sal first of all multiplied 6 times 3 to get a rectangular area that covered not only the trapezoid (its middle plus its 2 triangles), but also included 2 extra triangles that weren't part of the trapezoid. And that gives you another interesting way to think about it.

Area Of Trapezoids Rhombi And Kites Worksheet

Or you could also think of it as this is the same thing as 6 plus 2. 6 plus 2 divided by 2 is 4, times 3 is 12. Area of a trapezoid is found with the formula, A=(a+b)/2 x h. Learn how to use the formula to find area of trapezoids. Think of it this way - split the larger rectangle into 3 parts as Sal has done in the video. All materials align with Texas's TEKS math standards for geometry. Now, the trapezoid is clearly less than that, but let's just go with the thought experiment. Let's call them Area 1, Area 2 and Area 3 from left to right. What is the length of each diagonal? Adding the 2 areas leads to double counting, so we take one half of the sum of smaller rectangle and Area 2. A rhombus as an area of 72 ft and the product of the diagonals is.

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Either way, the area of this trapezoid is 12 square units. Aligned with most state standardsCreate an account. You're more likely to remember the explanation that you find easier. Maybe it should be exactly halfway in between, because when you look at the area difference between the two rectangles-- and let me color that in. Also this video was very helpful(3 votes). So it would give us this entire area right over there. 6 plus 2 times 3, and then all of that over 2, which is the same thing as-- and I'm just writing it in different ways. So, by doing 6*3 and ADDING 2*3, Sal now had not only the area of the trapezoid (middle + 2 triangles) but also had an additional "middle + 2 triangles". And it gets half the difference between the smaller and the larger on the right-hand side. Or you could say, hey, let's take the average of the two base lengths and multiply that by 3.

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What is the formula for a trapezoid? Well, that would be the area of a rectangle that is 6 units wide and 3 units high. 6th grade (Eureka Math/EngageNY). Created by Sal Khan. So what do we get if we multiply 6 times 3? 𝑑₁𝑑₂ = 2𝐴 is true for any rhombus with diagonals 𝑑₁, 𝑑₂ and area 𝐴, so in order to find the lengths of the diagonals we need more information. And this is the area difference on the right-hand side. How do you discover the area of different trapezoids? Okay I understand it, but I feel like it would be easier if you would just divide the trapezoid in 2 with a vertical line going in the middle. If you take the average of these two lengths, 6 plus 2 over 2 is 4. It should exactly be halfway between the areas of the smaller rectangle and the larger rectangle. The area of a figure that looked like this would be 6 times 3.

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So it completely makes sense that the area of the trapezoid, this entire area right over here, should really just be the average. Now, what would happen if we went with 2 times 3? So you could imagine that being this rectangle right over here. And I'm just factoring out a 3 here. Well, then the resulting shape would be 2 trapezoids, which wouldn't explain how the area of a trapezoid is found. And what we want to do is, given the dimensions that they've given us, what is the area of this trapezoid. It gets exactly half of it on the left-hand side. Hi everyone how are you today(5 votes). But if you find this easier to understand, the stick to it. So let's take the average of those two numbers. Access Thousands of Skills. So that would be a width that looks something like-- let me do this in orange. It's going to be 6 times 3 plus 2 times 3, all of that over 2. You could view it as-- well, let's just add up the two base lengths, multiply that times the height, and then divide by 2.

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At2:50what does sal mean by the average. This is 18 plus 6, over 2. Multiply each of those times the height, and then you could take the average of them. That is 24/2, or 12. That's why he then divided by 2. So when you think about an area of a trapezoid, you look at the two bases, the long base and the short base. Therefore, the area of the Trapezoid is equal to [(Area of larger rectangle + Area of smaller rectangle) / 2]. Well, now we'd be finding the area of a rectangle that has a width of 2 and a height of 3.

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You can intuitively visualise Steps 1-3 or you can even derive this expression by considering each Area portion and summing up the parts. Well, that would be a rectangle like this that is exactly halfway in between the areas of the small and the large rectangle. In Area 3, the triangle area part of the Trapezoid is exactly one half of Area 3. 5 then multiply and still get the same answer? Then, in ADDITION to that area, he also multiplied 2 times 3 to get a second rectangular area that fits exactly over the middle part of the trapezoid.

I hope this is helpful to you and doesn't leave you even more confused! This collection of geometry resources is designed to help students learn and master the fundamental geometry skills. Either way, you will get the same answer. So that is this rectangle right over here.

Why it has to be (6+2). Now let's actually just calculate it. If we focus on the trapezoid, you see that if we start with the yellow, the smaller rectangle, it reclaims half of the area, half of the difference between the smaller rectangle and the larger one on the left-hand side. That is a good question! 6 plus 2 is 8, times 3 is 24, divided by 2 is 12. So that's the 2 times 3 rectangle. In Area 2, the rectangle area part.

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