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

[@procash1968]

Super. Simple but well explained. Thanks 👍🙏

[@PreMath]

You are welcome Pracash 😊 You are the best. Keep it up dear 😃

[@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!

[@philipkudrna5643]

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…

[@PreMath]

Excellent Philip 👍 You are the best. Keep it up dear 😃

[@PreMath]

@@HackedPC Excellent Arkadeep. We are all proud of you 👍 You are the best. Keep it up dear 😃

[@vishalk4762]

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

[@bienvenidos9360]

The height of a triangle is a perpendicular line drawn from the base to the height of the triangle. The width of the rectangle = 5 which is also the height of the combined triangles using 8 as the base.

[@akxeman]

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

[@bienvenidos9360]

If a perpendicular line is drawn from the base of a triangle to the top, that is the height. So the side of the rectangle which is 5 would be the height.

[@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.

[@jayvantias4512]

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

[@bienvenidos9360]

The height of a triangle is a perpendicular line drawn from the base to the height of the triangle. The width of the rectangle = 5 which is also the height of the combined triangles using 8 as the base. Triangles A and B combine to form one triangle.

[@mariosamareta6349]

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?

[@albancal2002]

Exactly, that is what I thought : the height of that triangle is not 5... 🤔

[@bienvenidos9360]

To calculate the area of a triangle, the height would be the length of a perpendicular line drawn from the base of the triangle to the height of the triangle. So the width of the rectangle is perpendicular to the base of the triangle and extends to the length of the height of the triangle. So 5 would be the height used to calculate the area of this triangle with base 8.

[@misterenter-iz7rz]

The methods provided by you are very nice, for the equations are very simple.

[@mcbeaulieu]

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

[@nandisaand5287]

What? How can 5 be height?

[@bienvenidos9360]

The height of a triangle is a perpendicular line drawn from the base to the height of the triangle. The width of the rectangle = 5 which is also the height of the combined triangles.

[@MathChallenge1]

Premath, you always pick the most EPIC problems, thank you!! I recently started a KZbin 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! 🙏

[@PreMath]

Hello dear, we use Camtasia TechSmith utility. All the best. Take care😀

[@MathChallenge1]

Thank you so much!! 😊❤️

[@MathChallenge1]

@@PreMath sorry to bother again! Would you be able to recommend a mic that you use for recording? Thanks again!!

[@PreMath]

@@MathChallenge1 Blue Snowball iCE USB Mic Thanks for asking. Take care

[@MathChallenge1]

@@PreMath thank you!!

[@sameerqureshi-kh7cc]

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

[@PreMath]

Thanks Sameer dear You are the best. Keep it up dear😀 Stay blessed

[@luigipirandello5919]

Easy to understand your explanation. Thank you Sir.

[@DB-lg5sq]

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

[@om_ans]

اجمل بصمه ليكي حبيبتي مشاهده ممتعه ان شاء الله

[@PreMath]

شكرا لك يا عزيزي. أنت الأفضل. أبقه مرتفعا

[@mohamadrizaldunggio5070]

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

[@PreMath]

You are most welcome Rizal Excellent 👍 You are the best. Keep it up dear 😃

[@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

[@richardassal7788]

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

[@Aligakore]

So I went for a third method 😅. I have labelled the base of the small white rectangle triangle as « x » and its height « z ». The area we want to calculate is the area of the big rectangle triangle minus the area of the small one : (8+x)*5/2 - x*z/2 = 20 + 5*x/2 - x*z/2 The area we know equals to x*5/2 - x*z/2 = 6 When replacing this value in the first formula, the area we want to calculate is 20 + 6 = 26 square units 😊

[@sea34101]

Method 2 is nice!

[@PreMath]

Glad you think so! Excellent feedback 👍 You are the best. Keep it up dear 😃

[@DDX01]

Very nice

[@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.

[@nashsingh1349]

Exactly.... Something just doesn't make sense wrt the height (of 5....)

[@Reddogovereasy]

Yes, I too would like to know why 5 units is the height of triangle A.

[@bienvenidos9360]

The combined triangles A and B have base 8 and 5 is the width of the rectangle which also forms a perpendicular line to the base of the triangle and extends to the height of the combined triangles.

[@moretsphvlog5577]

Watching here to support

[@susennath6035]

Excellent

[@ロプノールs]

white triangle(big)=（8×５×１/２）-６＝14 . square(white+green)=8×５＝４０ green only Area=40-14=26 answer is 26

[@phanimaheswara7492]

Thank you sir

[@PreMath]

So nice of you Phani 👍 You are the best. Keep it up dear 😃

[@susennath6035]

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

[@bienvenidos9360]

Find the vertical height of the small white triangle using the green trapezoid/trapezium. Area of trapezoid = 1/2*height*(base1 + base2) 26= 1/2*8(5+x) X = 3/2 Then find the horizontal length of the small triangle. Small white triangle is proportional to bigger triangle (composed of combined areas of small white triangle and green trapezoid). Horizontal side/vertical side. Y/(3/2) = (y+8)/5 5y = 3y/2 + 24/2 Y = 24/7 Area = 1/2 base*height Area = 1/2(3/2)(24/7) Area = 18/7

[@kennethcook4826]

how is the height of Triangle a +triangle b =5

[@bienvenidos9360]

The height of a triangle is a perpendicular line drawn from the base to the height of the triangle. The width of the rectangle = 5 which is also the height of the combined triangles using 8 as the base. Triangles A and B combine to form one triangle.

[@Teamstudy4595]

Area of Green part = 26 square unit.

[@msafasharhan]

How the height of the traingle is 5 in first methode

[@bienvenidos9360]

The height of a triangle is a perpendicular line drawn from the base to the height of the triangle. The width of the rectangle = 5 which is also the height of the combined triangles using 8 as the base. Triangles A and B combine to form one triangle.

[@richardgratton7557]

Nice little problem. My only criticism is that the picture is nowhere near drawn to scale!

[@PreMath]

Thanks Richard for the feedback You are the best. Keep it up dear😀

[@willemkelles7942]

What a long way to get the solution. Triangle with base 8 has size 20. So area outside the yellow part is 14. Size of rectangle with long side 8 is 40. So green area is 40-14=26.

[@benjaminkarazi968]

Highlighted triangle: how 8 is the value of the height of this triangle?

[@bienvenidos9360]

8 is not the height. 8 is the base. The height is 5 which is the length of the side of the rectangle. He is calculating the area with the height for the combined triangles A & B. The height of a triangle is a perpendicular line drawn from a base to the height of the triangle.

[@benjaminkarazi968]

@@bienvenidos9360 The combination of triangles A and B is not a right triangle; could you try to determine the triangle's height inside? It cannot be 5.

[@bienvenidos9360]

It doesn't matter if the triangle has a right angle or not. The height to calculate the area of a triangle is the perpendicular distance from the base to a line parallel to the base that goes through the vertex of the opposite angle. So 5 = the height with 8 being the base. Since the side of the rectangle is at a 90° angle to the base, we can use the rectangle's width = 5 for the height to calculate the area since it meets a parallel line that goes through the vertex of the opposite angle to said base. We could use any of the other 2 sides for the base, but we already know the value for the height for the base 8. If we were to use the longest side of the triangle as the base, then that base = sqrt(7625/49) so the height would be about 3.2 to calculate area. If we were to use the remaining side as the base, then that length would be sqrt(1801/49) and the height using that base would be about 6.6

[@benjaminkarazi968]

@@bienvenidos9360 We are communicating in a different dimension. Could you just draw the height inside the triangle? What is your IQ?

[@bienvenidos9360]

The line for the height of the triangle doesn't always fit inside the triangle.

[@sirchedr]

easy

[@giuseppemalaguti435]

26

[@IITianTry2know]

26 square unit

[@PreMath]

Excellent Liltu 👍 You are the best. Keep it up dear 😃

[@IITianTry2know]

@@PreMath Thank you sir 😌😌🙂🙂

[@mustafizrahman2822]

Super question. But I have failed to solve it.

[@PreMath]

Thanks 👍 You are the best. Keep it up dear 😃

[@mustafizrahman2822]

@@HackedPC It's your wish.

[@mustafizrahman2822]

​@@HackedPC Actually Ib was very busy with my studies. And I haven't tried to solve it.

[@dennirodionov8642]

26,3125

[@JSSTyger]

A = 26 is my final answer.

[@thomakondaciu6417]

Sip e gjelbert del 23

[@anthonywaweru5969]

This is wrong triangle heights can't be 5

[@bienvenidos9360]

Yes the height is 5. The height of a triangle is a perpendicular line drawn from the base to the height of the triangle. The width of the rectangle = 5 which is also the height of the combined triangles using 8 as the base. Triangles A and B combine to form one triangle.

[@mustafizrahman2822]

1st

[@PreMath]

Great Mustafiz 👍 You are the best. Keep it up dear 😃

[@patrickakunna5366]

I used a different (3rd) method of similar triangles, area of triangles and area of a trapezoid to easily get the answer.

[@Deepsikhacreation]

40-14=26 simple...