Calculate total Area of all shaded triangles | Important Geometry skills explained | Fun Olympiad

[@devondevon4366]

Nice method, An alternative approach Let y= length of the large triangle and x= width, then the area of : green = [(y-7)(5)]/2 = (5y-35)/2 ( Since area of triangle = (length x width)/2 pink= [(x-5)(y-3)]/2 = ( xy-3x-5y + 15)/2 blue = [(3)(x-2)]/2 = (3x- 6)/2 yellow =14/2 Since area of the rectangle = the area of the green + pink + blue+ yellow + 35, then xy = green + pink + blue + yellow + 35 2xy = 5y-35 + (xy-3x-5y+ 15)+ (3x-6) + 14 + 70 (I multiply both sides by 2; hence xy becomes 2xy ; twos on the denominators are canceled and 35 becomes 70) 2xy = 5y-5y-3x+3x+xy-35-6 +15+ 14+ 70 2xy = -41+99 + xy 2xy-xy = 58 xy =58 So the total area of the triangle = 58 Area of the shaded triangles = 58-35= 23 Answer

[@mathpuzzles6352]

Great explanation! Thanks for making it!

[@vcvartak7111]

Truly creative solution

[@generaclesdey4622]

Clever approach!!

[@egillandersson1780]

Very interesting method ! I found the solution by another way : put x the length of the rectangle and y its height and calculate xy as the sum of the ' triangles + 35 : all simplifies but xy=58

[@sandanadurair5862]

Very interesting method indeed. Congrats!

[@HappyFamilyOnline]

Very well explained👍 Thanks for sharing🌺

[@Soumalya-j9j]

Thanks sir for teaching us good lesson

[@PreMath]

You are very welcome! Glad you think so! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

[@mega_mango]

English people are so pleasure

[@Waldlaeufer70]

That was a really clever approach! Thank you for sharing! :) P.S. By the way, your approach was - geometrically speaking - not "outside the box", but rather "inside the box". ;)

[@normanc918]

Thank you for video. Your explanation is good and clear.

[@Mani_yt77]

Thanks sir this is very nice problem and love from india♥️♥️♥️

[@PreMath]

You are very welcome! So nice of you, Manish You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

[@KAvi_YA666]

Thanks for video.Good luck sir!!!!!!!!!!!!!!!

[@PreMath]

Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

[@beeruawana6662]

Very good and interesting question sir Thank you so much 🙏🙏

[@bigm383]

Thanks Professor, I do like the way you recall even the most basic formulas as part of your process.

[@noahvale2627]

Ooh, loved this.

[@terapyo15]

Please bring videos on circles also

[@PreMath]

Sure. Keep watching. You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

[@alster724]

The grid part was tricky but I was able to catch it immediately

[@tompeled6193]

Is it possible to find the area of the individual triangles with only the given information?

[@Okkk517]

One way to find the solution to this problem as follows: taking BM=3 this leads to AE=0. Moreover letting DN=x we have 5*(x+7)-35=7+9/2+(5/2)*x. Solving for x we obtain x=23/5. Since the required area A=5*(x+7)-35=23 substituting the value of x we end up with A=23.

[@pramodsingh7898]

Thanks

[@easternbrown]

Interestingly, the problem is not sufficiently bound to determine the individual triangles. Rather the form of the whole can change without affecting the defined dimensions / area.

[@ib5299]

So clever

[@predator1702]

Very good solution 👍. Thank you teacher 🙏.

[@mega_mango]

OK, this one was interesting problem

[@TheVirtualWatcher]

I was trying to calculate each individual triangle area ... 🙄😂

[@stefanocarnicelli5323]

(Scrivo prima di vedere se il video)...Usando penna e righello (anche a mente) 35-((5-2)*(7-3))=23 (di ciascun triangolo traccio i segmenti paralleli ai cateti e tutto si capisce)

[@sandanadurair5862]

ShoeLace method Let EA be y and AF be x Coordinates E.......0. y F........x. 0 M.......x+3. y+3 N.......x-4. y+5 E. 0. y Using shoe lace rule S1 = 3xy + 8x -y + 15 S2 = 2xy + 3x -4y -12 Area EFMN = 1/2(S1-S2) EFMN = 1/2(XY + 5X + 3Y +27) Given EFMN = 35 1/2.(xy+5x+3y+27) = 35 Simplifying this we get xy + 5x + 3y. = 43......eq 1 Triangle areas P ..EAF. = xy/2 Q..EBM. = 3(y+3)/2 R..MCN = 7*2/2=7 S..NDE = (x-4).5/2 P+Q+R+S = 1/2(xy+5x+3y+3) Substituting eq.1 in above We get P+Q+R+S = 1/2(43 + 3) = 23

[@krzysz5023]

I spent way too much time trying to find the area of each triangle after I'd solved it 😂

[@angshukNag]

I found answer as 34 can't understand what went wrong. i can share you the steps on gmail if you want

[@PreMath]

sure. Thanks

[@giuseppemalaguti435]

L'area totale=58,

[@PreMath]

Thanks for sharing. You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀

[@devondevon4366]

23

[@larrydouglas9866]

I thought you were suppose to find the area of the original 4 shaded triangles, not including the 4 extras drawn to find the area of the little box. Thus the answer would be 11.5

[@sergiohqz]

Impossible rectangle.

[@halitiskender1324]

Müthiş bir çözüm

[@PreMath]

Böyle düşündüğüne sevindim! Geri bildiriminiz için teşekkürler! Şerefe! Harikasın Halit. devam et 👍 ABD'den sevgiler ve dualar! 😀 Mutlu kalın 😀