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### Course: Geometry (all content)>Unit 7

Lesson 7: Area of trapezoids & composite figures

# Area of trapezoids

Area of a trapezoid is found with the formula, A=(a+b)h/2. To find the area of a trapezoid, you need to know the lengths of the two parallel sides (the "bases") and the height. Add the lengths of the two bases together, and then multiply by the height. Finally, divide by 2 to get the area of the trapezoid. Created by Sal Khan.

## Want to join the conversation?

• What is the formula for a trapezoid?
• the formula to find the area of a trapezoid: (first base + second base) * height/2
• can't you just add both of the bases to get 8 then divide 3 by 2 and get 1.5 then multiply and still get the same answer?
• At what does sal mean by the average. Also this video was very helpful
• That is a good question!

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). Think of it this way - split the larger rectangle into 3 parts as Sal has done in the video. Let's call them Area 1, Area 2 and Area 3 from left to right. Notice that:

`1. In Area 1, the triangle area part of the Trapezoid is exactly one half of Area 1`
`2. In Area 2, the rectangle area part`` of the Trapezoid is equal to Area 2 as well as the area of the smaller rectangle. Adding the 2 areas leads to double counting, so we take one half of the sum of smaller rectangle and Area 2`
`3. In Area 3, the triangle area part of the Trapezoid is exactly one half of Area 3`

Therefore, the area of the Trapezoid is equal to [(Area of larger rectangle + Area of smaller rectangle) / 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. Either way, you will get the same answer.

Hope this helped.
• why it has to be (6+2).3/2? not (6-2).3/2?
(1 vote)
• I'll try to explain and hope this explanation isn't too confusing!
1. 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.
2. 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. In other words, he created an extra area that overlays part of the 6 times 3 area.
3. 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". That's why he then divided by 2.
I hope this is helpful to you and doesn't leave you even more confused!
• hi everyone how are you today
• a rhombus as an area of 72 ft and the product of the diagonals is
144. What is the length of each diagonal?
• 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.
• 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.
• Well, then the resulting shape would be 2 trapezoids, which wouldn't explain how the area of a trapezoid is found. But if you find this easier to understand, the stick to it. You're more likely to remember the explanation that you find easier.