Two Methods: Find the Area of the Green Trapezoid | Quick & Simple Tutorial

[procash]

Super. Simple but well explained. Thanks 👍🙏

[mahatmapodge]

First version is fairly simple, but second is elegant

[AdamjacobiGIA]

Solved it on sight with Method A, but I'm glad I clicked through to see the second method -- elegant and never would have occurred to me!

[JLvatron]

That was brilliant! So much easier than my solution of giving the small triangle (under the yellow triangle) base & height of X & Y.
Then use the 3 similar triangles to get relation formulas, and the yellow area to be 6= 1/2 * x * (5-y).
Solve several of these equations together to get X, Y, then 2 triangle areas to calculate the area difference.
Yup, the Long way.

[mariosamareta]

You combined triangles A + B and made not a right triangle. You made the base 8 and height 5, but height of 5 went beyond combined triangles. How could it be? Also the base should be the line from bottom left to the upper right?

[akxeman]

I’d like to see how it was determined the height of AB=5

[philipkudrna]

Before watching: the area of the green region is 26 square units: let‘s call the missing part of the left triangle „A“ and the green area „B“. Also the missing base of the leftisms triangle is „x“. It follows that A+B= (8+x)*5/2 and 6+A=5x/2. if we substitute for A=(5x/2)-6 into the first equation, 5x cancels and B=26.
Ok, you called the areas with different letters, so my B is your C in your first solution. Anyways, your first method is much simpler, And also the second method is very elegant. I like it! Seems my approach, even though successful, was unnecessarily complicated…

[vishalk]

In first method, how can height of triangle be 5 units?

[sameerqureshi-khcc]

Awesome! Sir you are a genius mathematician! Love from Pakistan 🌹🌹🌹🌹

[MathChallenge]

Premath, you always pick the most EPIC problems, thank you!!
I recently started a YouTube channel myself, with math problems geared more for elementary kids.
Can I ask you how you film your videos?
I have been filming using Zoom calls and a computer whiteboard, but the screen always turns out a bit fuzzy.
Thank you humbly for your advice! 🙏

[jayvantias]

How the height of triangle in first method is 5??

[DB-lgsq]

شكرأ لكم على المجهودات
يمكن استعمال a اصغر زاوية داخلية في B وb اصغر ضلع فيB
tan a =8/5-b
6=1/2 . b/cos a.(5-b)sina =4b
b=3/2
S=[(3/2 +5).8]/2 =26

[mcbeaulieu]

I tried myself before watching and I ended up using your 1st method. I love your content, keep it up my friend 💪😊👌

[luigipirandello]

Easy to understand your explanation. Thank you Sir.

[mohamadrizaldunggio]

Thanks sir. Well explained, i'm inspired and challenge my self to solve it another way.

[Om_omer-z]

اجمل بصمه ليكي حبيبتي مشاهده ممتعه ان شاء الله

[theoyanto]

Just never saw it, hiding triangles in geometry, cool Idea 😁
Note to self
"always rotate drawings for better observation "
I guess I just had an episode of triangle blindness,
Annoying that I didn't see such a simple solution

[richardassal]

How do you know that the top edge is parallel to the bottom line? It is not given.

[susennath]

Pls calculate area B mentioned in second case which is also below the 6 sq unit trangle

[Reddogovereasy]

Please define the height of a triangle. From my limited knowledge, the height has to be from a perpendicular point, forming a right angle, on the base to the top opposite that base. Please correct my thinking by defining the height of a triangle.