Visualizing Area of a Trapezoid Formula - Deriving the Formula

tapintoteenmind... Understanding where the formula for area of a trapezoid comes from is essential in developing a deep understanding. This video uses visualizations to show 3 different versions of the formula which scaffold from splitting the trapezoid into two triangles, all the way to the formula most textbooks teach our students to use.

[@bloomyfractal3585]

Thanks to this video, the formula makes much more sense ! Thanks a lot to you !

[@leocomerford]

2:27 This tactic is only visibly correct when the trapezoid is isosceles, and even in that case it's not quite self-evident that the bh/2 rectangle will split into an ah/2 rectangle and a rectangle whose base is of equal length to the bases of the triangles on the sides. To give a visualisation that works nicely for any non-obtuse trapezoid, you can divide the ah and bh rectangles vertically rather than horizontally. Then the ah/2 rectangle can be dropped on top of the bh/2 rectangle so that its top edge coincides with a. Then it's just a matter of tidying up the two rectangles (or one rectangle) not covered by a into triangles. Futher, the obtuse-trapezoid case-where a and b have some overlap, at least-can be covered by starting with an obtuse trapezoid, then converting it into an acute or right trapezoid of equal area by flipping the overhanging side. Obtuse trapezoids with non-overlapping a and b would be a good place to introduce the alternative two-triangles approach...

[@delphinithedarklordsaugurey]

nice
im confused tho

[@tthirupathy]

More and clear explanations are necessary for beginners. This video will be useful for self learning. It's good.

[@shalinithakur1489]

Should get teacher's Nobel prize for this

[@KylePearceMathlete]

Too kind! Thanks for stopping by!

[@shyampaldahiya2134]

Excellent way of teaching..keep it up

[@KylePearceMathlete]

Thanks! Have a great day!

[@YouAdrianziom]

I used a different method to come to the same conclusion. You convert the trapezoid into 3 rectangles, split the ones on the sides to make the arms (cause splitting a rectangle in half diagonally means calculating the area of a triangle). Take the middle rectangle out for now and bring the arms together forming another triangle (they are the same height), so we can simplify things. Now the base of that triangle is basically ((b-a)*h)/2 + the rectangle we discarded a*h. When you reduce everything you get (a+b)*h/2. Doesn't look that neat, but imo easier to understand

[@mayjack]

Damn, that's the stuff for someone to write thesis on trapezium or trapezoid 😅👍

[@aabbe762]

Thank you sir

[@jackchan6266]

well explained, great visual!

[@reneenfaizal5163]

Such a logical explanation

[@janicknorman9396]

Thank you so much

[@KylePearceMathlete]

Thanks so much for the feedback!

[@daisy_blue1235]

You are good tracher with deep knowledge but by using formula trapezoid is rally simple n easy which ur extra explanations has made really complicated plz ley easy thing simple

[@KylePearceMathlete]

Thanks for the feedback! Just trying to provide multiple perspectives. Sometimes, that might make things appear to be more complicated, but I believe the more representations the better!

[@Unknown-nv5ro]

Thank you kyle, you know I always hate to take things as they are, Like "just use the formula", I love to Understand why this formula is the FORMULA to USE, and this is something that is missing from traditional school, "Just use the formula" without understanding why we use exactly that formula and how it was being constructed and how it solves the puzzle, it's easy to get confused by this, but it's beautiful to understand it all by seeing it Right infront of you. thanks again.

[@KylePearceMathlete]

blackdiamondtheonful appreciate you taking the time to comment! Glad you found it helpful!

[@Ashishkumar-hp6js]

how did you created this video?

[@ivandrofly]

Thank you!

[@satya-ek3jx]

u r the best...

[@KylePearceMathlete]

Thanks!

[@danielaadriatico5966]

1:39 it looks like a bed

[@wchi8391]

This is genius

[@KylePearceMathlete]

God Emperor thanks! Glad to hear it was helpful!!