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Think of it this way - split the larger rectangle into 3 parts as Sal has done in the video. So we could do any of these. 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. Either way, you will get the same answer.

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Access Thousands of Skills. You can intuitively visualise Steps 1-3 or you can even derive this expression by considering each Area portion and summing up the parts. 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. The area of a figure that looked like this would be 6 times 3. So that would give us the area of a figure that looked like-- let me do it in this pink color. So what would we get if we multiplied this long base 6 times the height 3? Texas Math Standards (TEKS) - Geometry Skills Practice. 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". Well, that would be the area of a rectangle that is 6 units wide and 3 units high.

That's why he then divided by 2. In other words, he created an extra area that overlays part of the 6 times 3 area. Now, the trapezoid is clearly less than that, but let's just go with the thought experiment. And what we want to do is, given the dimensions that they've given us, what is the area of this trapezoid. In Area 3, the triangle area part of the Trapezoid is exactly one half of Area 3.

A width of 4 would look something like that, and you're multiplying that times the height. Let's call them Area 1, Area 2 and Area 3 from left to right. And so this, by definition, is a trapezoid. Or you could say, hey, let's take the average of the two base lengths and multiply that by 3. 6 6 skills practice trapezoids and sites on the internet. What is the length of each diagonal? Now, it looks like the area of the trapezoid should be in between these two numbers. Well, then the resulting shape would be 2 trapezoids, which wouldn't explain how the area of a trapezoid is found. 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. Why it has to be (6+2). So let's take the average of those two numbers.

Lesson 3 Skills Practice Area Of Trapezoids

So right here, we have a four-sided figure, or a quadrilateral, where two of the sides are parallel to each other. So let's just think through it. So it completely makes sense that the area of the trapezoid, this entire area right over here, should really just be the average. Aligned with most state standardsCreate an account. In Area 2, the rectangle area part. 6 6 skills practice trapezoids and kites answer key. I'll try to explain and hope this explanation isn't too confusing! Now, what would happen if we went with 2 times 3? Well, now we'd be finding the area of a rectangle that has a width of 2 and a height of 3. That is 24/2, or 12.
Hi everyone how are you today(5 votes). So that would be a width that looks something like-- let me do this in orange. Now let's actually just calculate it. 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. It should exactly be halfway between the areas of the smaller rectangle and the larger rectangle.

I hope this is helpful to you and doesn't leave you even more confused! And that gives you another interesting way to think about it. Our library includes thousands of geometry practice problems, step-by-step explanations, and video walkthroughs. All materials align with Texas's TEKS math standards for geometry. But if you find this easier to understand, the stick to it.

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So you could imagine that being this rectangle right over here. Of the Trapezoid is equal to Area 2 as well as the area of the smaller rectangle. So it would give us this entire area right over there. Or you could also think of it as this is the same thing as 6 plus 2. Lesson 3 skills practice area of trapezoids. If you take the average of these two lengths, 6 plus 2 over 2 is 4. These are all different ways to think about it-- 6 plus 2 over 2, and then that times 3. 6 plus 2 divided by 2 is 4, times 3 is 12. Adding the 2 areas leads to double counting, so we take one half of the sum of smaller rectangle and Area 2.

It's going to be 6 times 3 plus 2 times 3, all of that over 2. And this is the area difference on the right-hand side. This collection of geometry resources is designed to help students learn and master the fundamental geometry skills. It gets exactly half of it on the left-hand side. That is a good question! 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.

So what Sal means by average in this particular video is that the area of the Trapezoid should be exactly half the area of the larger rectangle (6x3) and the smaller rectangle (2x3).
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