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And this is the area difference on the right-hand side. I'll try to explain and hope this explanation isn't too confusing! Or you could also think of it as this is the same thing as 6 plus 2. So it would give us this entire area right over there. Aligned with most state standardsCreate an account. Now let's actually just calculate it. You can intuitively visualise Steps 1-3 or you can even derive this expression by considering each Area portion and summing up the parts. Hi everyone how are you today(5 votes). Now, it looks like the area of the trapezoid should be in between these two numbers. What is the length of each diagonal? It should exactly be halfway between the areas of the smaller rectangle and the larger rectangle. Either way, the area of this trapezoid is 12 square units. How do you discover the area of different trapezoids?
This collection of geometry resources is designed to help students learn and master the fundamental geometry skills. At2:50what does sal mean by the average. 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. These are all different ways to think about it-- 6 plus 2 over 2, and then that times 3. 5 then multiply and still get the same answer? Well, now we'd be finding the area of a rectangle that has a width of 2 and a height of 3. In other words, he created an extra area that overlays part of the 6 times 3 area. So right here, we have a four-sided figure, or a quadrilateral, where two of the sides are parallel to each other. You could also do it this way. Let's call them Area 1, Area 2 and Area 3 from left to right. In Area 2, the rectangle area part. 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. So these are all equivalent statements.
That's why he then divided by 2. So we could do any of these. 6 plus 2 is 8, times 3 is 24, divided by 2 is 12. So when you think about an area of a trapezoid, you look at the two bases, the long base and the short base. So you could imagine that being this rectangle right over here. 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. And what we want to do is, given the dimensions that they've given us, what is the area of this trapezoid. And that gives you another interesting way to think about it. You're more likely to remember the explanation that you find easier.
Well, then the resulting shape would be 2 trapezoids, which wouldn't explain how the area of a trapezoid is found. 6 plus 2 divided by 2 is 4, times 3 is 12. Access Thousands of Skills. So that would be a width that looks something like-- let me do this in orange. Therefore, the area of the Trapezoid is equal to [(Area of larger rectangle + Area of smaller rectangle) / 2]. Multiply each of those times the height, and then you could take the average of them. Adding the 2 areas leads to double counting, so we take one half of the sum of smaller rectangle and Area 2. A width of 4 would look something like that, and you're multiplying that times the height. A width of 4 would look something like this. Why it has to be (6+2). I hope this is helpful to you and doesn't leave you even more confused! 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. So that's the 2 times 3 rectangle. So you could view it as the average of the smaller and larger rectangle.
So that would give us the area of a figure that looked like-- let me do it in this pink color. 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. And I'm just factoring out a 3 here. 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. That is a good question!
If you take the average of these two lengths, 6 plus 2 over 2 is 4. Created by Sal Khan. Also this video was very helpful(3 votes). 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". 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.
The area of a figure that looked like this would be 6 times 3. Now, the trapezoid is clearly less than that, but let's just go with the thought experiment. Well, that would be a rectangle like this that is exactly halfway in between the areas of the small and the large rectangle. And so this, by definition, is a trapezoid. Of the Trapezoid is equal to Area 2 as well as the area of the smaller rectangle. So you multiply each of the bases times the height and then take the average.
But if you find this easier to understand, the stick to it. Or you could say, hey, let's take the average of the two base lengths and multiply that by 3. Our library includes thousands of geometry practice problems, step-by-step explanations, and video walkthroughs. 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. Can't you just add both of the bases to get 8 then divide 3 by 2 and get 1. Well, that would be the area of a rectangle that is 6 units wide and 3 units high. So it completely makes sense that the area of the trapezoid, this entire area right over here, should really just be the average. Think of it this way - split the larger rectangle into 3 parts as Sal has done in the video. 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. In Area 3, the triangle area part of the Trapezoid is exactly one half of Area 3. So let's just think through it.
It's going to be 6 times 3 plus 2 times 3, all of that over 2. How to Identify Perpendicular Lines from Coordinates - Content coming soon. That is 24/2, or 12. All materials align with Texas's TEKS math standards for geometry.
6th grade (Eureka Math/EngageNY). And it gets half the difference between the smaller and the larger on the right-hand side.