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.
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.
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 ❤❤❤
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.
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 .
we know the base of the new triangle is a straight line because it is composed of supplementary angles (we know those angles are supplementary because, in the original trapezoid, they are also consecutive interior angles of a transversal between parallel lines) we know the other two sides of the triangle form straight lines with the rest of the diagram because they were constructed by a 180 degree rotation of an angle.
My teacher taught me to draw a line from bottom left corner to top right corner, to cut the trapezoid into 2 triangles as well, then the area of it is exactly the sum of 2 triangles.
The urge to use pythagorean theorem when it transformed into the triangle.
I hear you friend...😢
Me too brother
I always thought of it as the average length of the trapezium, forming a rectangle of uniform length and width
Nice way too of course :)
Now that makes me think - what shape's areas can be found using different means, such as harmonic or geometric?
@@catmacopter8545you're into something
I’ve never heard of the word “trapezium,” but it fully explains the name “trapezoid”
@@Barnil_JN that is exactly what i said
Ohhhh!! That's why!! I finally know the reason for that formula!! 💗
👍
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.
Solid proof 💯 keep going! 👍
I have a Math degree and never thought to look up how this formula was created. Good stuff
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.
We learned, to double it into a parallelogram, and then /2 to get the trapezoid formula
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 ❤❤❤
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.
Join any diagonal , now there are triangles with height. Find their area and take out 1/2 and height common
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 😄
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 .
my logic was get 2 identical copies, arrange them into a paralellogram sideways and calculate THAT before deviding the whole thing by 2
A good way!
@@MathVisualProofs thank you :)
Heyoooo I had the same idea. Nice, man
I wonder if the formula to find a trapezoid’s area is just how you find the area of any quadrilateral
how do we know that the larger triangle is straight line?
we know the base of the new triangle is a straight line because it is composed of supplementary angles (we know those angles are supplementary because, in the original trapezoid, they are also consecutive interior angles of a transversal between parallel lines)
we know the other two sides of the triangle form straight lines with the rest of the diagram because they were constructed by a 180 degree rotation of an angle.
My teacher taught me to draw a line from bottom left corner to top right corner, to cut the trapezoid into 2 triangles as well, then the area of it is exactly the sum of 2 triangles.
Cemu sve to, odakle to sada Pitagorim teorem, to nas u skoli nisu ucili!
Maa Shaa Allaaaaah
Woooo
Is b1 and b2 should be parallel?
Yes. That’s important part of a trapezoid.
So trapezoid is righ triangle
here before 30 likes
Why?
why author liked me?
@@Why553-k5b_1 Dunno