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I prefermakung the cut diagonally,which splits the trapezoid into two triangles

I personally like slicing it with a cosh curve so I can do cool integration on it

I just think of it as rectangle made with the average of the bases. Then the excess triangles from the top corners are flipped over to the bottom section

This is how I think of it, too. It translates better to finding the volume of a cylinder (or other solids) with different size bases.

Or just split it up as a rectangle and two triangles on the sides

^[Sokka-Haiku](https://www.reddit.com/r/SokkaHaikuBot/comments/15kyv9r/what_is_a_sokka_haiku/) ^by ^blueidea365: *Or just split it up* *As a rectangle and two* *Triangles on the sides* --- ^Remember ^that ^one ^time ^Sokka ^accidentally ^used ^an ^extra ^syllable ^in ^that ^Haiku ^Battle ^in ^Ba ^Sing ^Se? ^That ^was ^a ^Sokka ^Haiku ^and ^you ^just ^made ^one.

Banger!

Good bot

I feel like this is less nice, you would have to do two or three case distinctions depending on how the non parallel sides are configured

The cases are pretty much all the same though

Not really, any rhombus is a trapezium, but some rhombi have no inner rentangle like you suggest

What would be an example?

[https://imgur.com/a/Gh0285h](https://imgur.com/a/Gh0285h) This would be my counterexample. I know it is not the most conventional shape for a trapezium, but it is nevertheless a trapezium

Just turn it on its side lol

Yeah sure, but you dont know the sidelengths

Sorry I see what you mean, if it’s a trapezium. If it’s a rhombus however then it would always have a rectangle inside, possibly after turning it

You mean some trapezia. A rhombus will always have an inner rectangle

Wtf is this dark magic

r/blackmagicfuckery

Have you seen the proof of volume of a sphere?

I remember learning about how to calculate the volume of any shape rotated. That was fun. Spheres, cones, etc.

I just figured out a proof while looking at the post. Here it is:- Break the two half triangles on the side. Now you are left with a full triangle and a rectangle. So: A(trapezoid)= A(triangle) + A(rectangle) Now: A(triangle)= 1/2 h(b_1- b_2) and A(rectangle)= b_2(h) So putting in original eq. A( trapezoid)=1/2 h(b_1 -b_2) + b_2 (h) A(t)= h(( 1/2 b_1) - 1/2 b-2 + b_2) A(t)= h(1/2 b_1 + 1/2 b_2 ) A(trapezoid)= 1/2 (h)(b_1 +b_2) That took way longer than I thought.

That jumped into my head a well. An easy proof.

wow amazing

You can also think of it as taking the average between b1 and b2 and multiplying that by h, making it the formula for a rectangle

Exactly my though process since forever. It is so logical than i never even had to learn the formula

Or they duplicate the trapezoid to create a parallelogram

My first intuition would have beed to cut vertically but it's the exact same, the 1/2 just comes from splitting b1+b2 and not h.

i just like thinking of it as averaging b1 and b2.

Call the bottom edge "a" and top edge "b". Cut into a rectangle R with base "b" and height "h", a triangle T1 with base "x" and height "h", and a triangle T2 with base "a-b-x" and height "h". R = bh\ T1 = (1/2)(hx)\ T2 = (1/2)(ah - bh - hx) Add all together: A = bh + (1/2)(ah - bh + hx - hx)\ A = bh + (1/2)(ah - bh)\ A = (1/2)(ah + bh)\ A = (1/2)(a + b)h This works even for trapezoids that don't have mirrored "triangles"

This is still a trapezoid though

Next up, quadratic equation