5 then multiply and still get the same answer? Now, what would happen if we went with 2 times 3? At2:50what does sal mean by the average. Well, that would be a rectangle like this that is exactly halfway in between the areas of the small and the large rectangle. So when you think about an area of a trapezoid, you look at the two bases, the long base and the short base. So these are all equivalent statements.
It gets exactly half of it on the left-hand side. Therefore, the area of the Trapezoid is equal to [(Area of larger rectangle + Area of smaller rectangle) / 2]. 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. It should exactly be halfway between the areas of the smaller rectangle and the larger rectangle. 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. What is the length of each diagonal? I'll try to explain and hope this explanation isn't too confusing! So you could imagine that being this rectangle right over here. So let's take the average of those two numbers. In Area 2, the rectangle area part. 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. A rhombus as an area of 72 ft and the product of the diagonals is.
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. 6th grade (Eureka Math/EngageNY). 6 plus 2 is 8, times 3 is 24, divided by 2 is 12. Created by Sal Khan. And this is the area difference on the right-hand side. In other words, he created an extra area that overlays part of the 6 times 3 area. So it completely makes sense that the area of the trapezoid, this entire area right over here, should really just be the average.
A width of 4 would look something like that, and you're multiplying that times the height. So right here, we have a four-sided figure, or a quadrilateral, where two of the sides are parallel to each other. Hi everyone how are you today(5 votes). So what would we get if we multiplied this long base 6 times the height 3? You're more likely to remember the explanation that you find easier. If you take the average of these two lengths, 6 plus 2 over 2 is 4. What is the formula for a trapezoid? Either way, you will 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. So that would be a width that looks something like-- let me do this in orange. This collection of geometry resources is designed to help students learn and master the fundamental geometry skills. So that would give us the area of a figure that looked like-- let me do it in this pink color. 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.
These are all different ways to think about it-- 6 plus 2 over 2, and then that times 3. Either way, the area of this trapezoid is 12 square units. How do you discover the area of different trapezoids? The area of a figure that looked like this would be 6 times 3. Of the Trapezoid is equal to Area 2 as well as the area of the smaller rectangle. Now, the trapezoid is clearly less than that, but let's just go with the thought experiment. Well, then the resulting shape would be 2 trapezoids, which wouldn't explain how the area of a trapezoid is found. So let's just think through it. So we could do any of these. That's why he then divided by 2. So you multiply each of the bases times the height and then take the average. Multiply each of those times the height, and then you could take the average of them.
It's going to be 6 times 3 plus 2 times 3, all of that over 2. And it gets half the difference between the smaller and the larger on the right-hand side. 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). You could also do it this way. And so this, by definition, is a trapezoid. Can't you just add both of the bases to get 8 then divide 3 by 2 and get 1. Why it has to be (6+2). Now let's actually just calculate it.
Adding the 2 areas leads to double counting, so we take one half of the sum of smaller rectangle and Area 2. Aligned with most state standardsCreate an account. Think of it this way - split the larger rectangle into 3 parts as Sal has done in the video. This is 18 plus 6, over 2. You can intuitively visualise Steps 1-3 or you can even derive this expression by considering each Area portion and summing up the parts. Our library includes thousands of geometry practice problems, step-by-step explanations, and video walkthroughs. I hope this is helpful to you and doesn't leave you even more confused!
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Party planning couldn't be easier with candy by color selections of hard candy, gummies, M&M's, jelly beans, sour candy, and a rainbow of foil wrapped chocolates. 4 Hours of Cleaning. Check out our informational series of short videos and infographics to learn how to make your own DIY successful candy buffet. Something like Hershey's strawberry syrup, or a strawberry glaze (fruit dip) from the produce section of the grocery store works great.
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