Trapezoid Area Visual Proof

This is a short animation showing a standard fact about how to find the area of a trapezoid by finding a triangle with the same area.

Here is the original video in wide-format, wordless, with dramatic music:

Here is a related visual proof for the area of a parallelogram:

#area #triangle #trapezoid #geometry #visualproof #math #manim

This video was inspired by a beautiful GeoGebra applet created by Tim Brzezinski:

To learn more about animating with manim, check out:

[Kofhiliphus]

The urge to use pythagorean theorem when it transformed into the triangle.

[isaacdiboss]

I always thought of it as the average length of the trapezium, forming a rectangle of uniform length and width

[mitsunam]

Ohhhh!! That's why!! I finally know the reason for that formula!! 💗

[meflea]

I mean another good method is to duplicate the trapezium and then flip it vertically. That when you fit the two trapezium together, you'll get a parallelogram.

Meaning that a trapezium is just half the area of a parallelogram and a parallelogram is twice the area of a trapezium.

[Zangoose_]

I have a Math degree and never thought to look up how this formula was created. Good stuff

[discreaminant]

Another way is to double the trapezoid and combine them… kinda like how u would visualize triangle’s area
This’s what my previous textbook does 😄

[DeshBhakt-tc]

I went to see everywhere why this formula makes sense and all of them were unable to explain this to me but you are the one who easily satisfied with no doubt in my head now ❤❤❤

[sabiraakther]

If we put two trapezium one is right way another one is upside down together we found a parallelogram at the topside is b2+b1 and at the bottom is b1+b2 base = b1+b2. Formula of the parallelogram is bh
If we put trape(Parll)= (b1+b2)h
If we put real trapezium which is half of parallelogram is ((b1+b2)h)/2
Henzed proof.

[janemeier]

We learned, to double it into a parallelogram, and then /2 to get the trapezoid formula

[seiraeziar]

how do we know that the larger triangle is straight line?

[rajkotalovic]

Cemu sve to, odakle to sada Pitagorim teorem, to nas u skoli nisu ucili!

[keescanalfp]

stunning . but why would any teacher like to make disappear both that turning point and that sommation point of b1+b2.
we would like to see both of them in the resulting figure, please, please ! some seconds longer .

[fanamatakecick]

I wonder if the formula to find a trapezoid’s area is just how you find the area of any quadrilateral

[TheDHemant]

Join any diagonal, now there are triangles with height. Find their area and take out 1/2 and height common

[mxsteri]

my logic was get 2 identical copies, arrange them into a paralellogram sideways and calculate THAT before deviding the whole thing by 2