Area of a trapezoid | Perimeter, area, and volume | Geometry | Khan Academy

A trapezoid is a cousin of the parallelogram. However, in trapezoids only two of the opposing sides are parallel to each other. Here we explain how to find its area.

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[decarbonized]

If you're still confused, just add both of the base numbers and multiply it by the height and then divide by two.

[michaelmag]

Thank you for starting this with a thought experiment. It really helps to understand why the equation is built the way it is.

[RashedAhmad]

There is a much easier way to do it. Draw a diagonal line. You'll have two triangles, thus, the sum of the areas of the two triangles would be the answer, i.e., (1/2 x 6 x 3) + (1/2 x 2 x 3) = 12

[NeverHumorous]

Watched this while listening to "The Poem of Everyone's Souls" from Persona 5 and that makes this seem hella dramatic!

[skrumb]

Apply the same thing you learned for the triangles, flip it and make a parallelogram with it and divide it by two.. It's much easier. Base A + Base B * Height / 2

[tavian_]

Thank you khan, I actually understand, randy palisoc didn’t help but you actually explained it so thank you.

[donwilson]

2:14 - 2:30 That's a big jump between calculating the areas of the edges of the trapezoid and "taking the average of both".

[anahata]

This is the most convoluted and inscrutable video you have ever assembled.

[mulimotola]

I understand it like this - when you divide the whole rectangle area in half, you get one of the triangles on each side of the trapezoid, plus half of the middle rectangle, so you compensate by taking the other half of the middle rectangle.

[lyan]

hmm I solved it by first taking the whole area (6*3) and then I imagined reforming the trapezoid so that the left line segment is vertical. now it's clear that the missing area on the right would be ((6-2)*3)/2 and therefore (6*3)-((4*3)/2)...so formula would be bottom * height - |(bottom-top)|*height

[abdulrafiq]

Thank for every one❤
We pleased take your recording class

[TasyaAdzkiya]

OK, I think I got it, but please correct me if I'm wrong.

I think the reason behind the notion that we have to take the average of the larger rectangle and the smaller rectangle is that imagine if you cut the larger rectangle in half and cut the smaller rectangle in half and arranged the half of the larger rectangle and the half of smaller rectangle, you will get a trapezoid!

To make it more obvious, don't forget to draw dotted line of the smaller rectangle inside of the trapezoid first. Then, you can draw dotted line around the trapezoid to make it look like it is inside of a larger rectangle. You can arrange the other half of the smaller rectangle (from taking the average of the smaller triangle inside of the trapezoid) to make the other half of the smaller rectangle that you've got from splitting the bigger rectangle complete. After that, you can arrange the rectangle outside of the trapezoid that you've got from splitting up the larger rectangle and place it on the other side of the trapezoid that doesn't have "wing" or triangle on its side, yet. And, you're done!

You can verify it by looking at the example and the computation that Sal did.
(6×3 + 2×3)/2 is the same as (6×3)/2 + (2×3)/2
So, splitting up the larger rectangle and the smaller rectangle, and rearranging the halves of them seems legitimate.

Also, you can imagine that if you only compute the average/split up the larger rectangle, you wouldn't get a trapezoid. The same goes with if you only compute the average/split up the smaller rectangle, you wouldn't get a trapezoid.

[ranchoconstruction]

How do you calculate the area and volume of an non-parallelogram trapezoid, where you have different leg height?

Example 1
B1=15, B2=25 and h=5
Area=? V=?

Example 2
B1=15, B2=25, h1=5 and h2=6
Area=? V=?

I wonder if you can explain? 🤔

[feiyinwang]

First time, I understand why the formula looks like how it is!

[itzpurple]

This helped me but the easier format would just be H (b1+b2)

2

[MrMarkgyuro]

this kinda explanations really makes me excited about math :)

[albertdu]

lmao I think this is one of the more confusing videos. I do like kahn though but for anyone whos confused I would just separate the two rectangles from the middle one and get the side of those two rectangles being b-a and h for the purple rectangles and a and h for the middle rectangle then do 1/2 (b-a)* h for the purple half and then add to a*h for the middle one. Or you can just turn the trapezoid into two triangles and you will see 1/2 b* h +1/2 a*h is answer lol thats the easiest way

[tineetech]

Thank you so much for helping me with my math

[interstateruler]

Sal, I was hoping to see the formula of the area of a trapizoid

[aliplays]

i am a grade 6 boy and u give me this dude hard to revise lol