Find area of the Rectangle ABCD | Blue shaded triangle area is 405 | Important skills explained

[@rishudubey1533]

thank u dear 😊

[@PreMath]

You are very welcome! So nice of you. Thank you! Cheers! 😀

[@robertakerman3570]

@@PreMath I can't actually do the math, but UR Xplanations R easy to follow.

[@procash1968]

Addicted to your videos in geometry..... This is a good addiction & a super stress relief

[@PreMath]

Happy to hear that! Stay blessed, dear🙏

[@spiderjump]

Let CB = b 1/2•12•15 +405 +1/2•30•b =1/2(12+b)•45 90+405+15b=270+22.5b b=30 Area =45•30=1350

[@santiagoarosam430]

El segmento vertical FG y el horizontal por EH se cortan en el punto “O” y el rectángulo queda dividido en cuatro rectángulos → ABCD=AFOE+FBHO+EOGD+OHCG → AF=45-30=15→AFOE=15*12=180 → FBHO=30*12=360 → EOGD=2*[405-(180/2)-(360/2)]=2*135= 270 → AD =AE+ED=12+(270/15)=12+18=30 → ABCD=45*30 =1350 Ud² . Gracias y saludos.

[@MultiYesindeed]

Thanks for your great work again

[@PreMath]

Thanks again!

[@KAvi_YA666]

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

[@PreMath]

You are awesome. Keep it up 👍

[@anahimaceda7070]

Awesome!!! 😊 Thanks!

[@PreMath]

Our pleasure!

[@unknownidentity2846]

There is an interesting alternative: The vectors v(CE) and v(CF) can be written as: v(CE) = ( −45 ; 12−y ) v(CF) = ( −30 ; −y ) The known area of the blue triangle can now be expressed by the cross product of these two vectors: A(CEF) = (1/2) * |v(CE) x v(CF)| = (1/2) * |45y + 30(12−y)| = (1/2) * |15y + 360| = (1/2) * (15y + 360) # since y > 0 (1/2) * (15y + 360) = 405 15y + 360 = 810 15y = 450 y = 30🙂 Best regards from Germany

[@alster724]

Nice geometry problem. Super easy

[@PreMath]

Yes, thanks

[@Abby-hi4sf]

As usual great lesson

[@PreMath]

Thank you again

[@burlfromlondon]

Would have preferred to collect all like terms before multiplying by 2

[@PreMath]

Thank you! Cheers! 😀

[@nmg1909]

Different styles for different people. Just know the rules and formula.

[@mohabatkhanmalak1161]

More than one road lead to Rome!

[@kennethstevenson976]

I used (x+12) for the width and got x=18 which produces the same Area =( x+12) x 45 = (18+12)x45= 1350 cm.^2

[@giuseppemalaguti435]

15*12/2+405+30h/2+45(h-12)/2=45h...h=30...A=45*30

[@josealmariferreiraferrreir3374]

👏👏👏👏👏

[@PreMath]

You are awesome. Keep it up 👍

[@misterenter-iz7rz]

Let DE be a, BC be a+12, the area of the rectangle is 45x(a+12), and 405=45a+12x45-12x15/2-30x(a+12)/2-45a/2, so 810=90a+24x45-12x15-30a-30x12-45a, 15a=810-24x45+12x15+30x12=270, a=270/15=18, hence the answer is 45x30=1350.😊

[@JSSTyger]

A=(30+x)(12+y) =(1/2)(12x)+(1/2)(30)(12+y)+(1/2)(45y)+405

[@vidyadharjoshi5714]

45*BC = 405 + 0.5*[ DC*DE + AE*AF + BF*BC] = 405 + 0.5*[ (45*(BC-12) + 12*15) + 30*BC ] = 405+15BC + 22.5*BC - 180. 7.5*BC = 225; BC = 30. ABCD Area = 45*30 = 1350

[@mohamadtaufik5770]

1350 cm^2

[@prossvay8744]

Area of rectangle ABCD=45×30=1350

[@Micboss1000]

Could've skipped calculating y and gone straight from 15y to 45y, since you only need the area.

[@prossvay8744]

S=1350cm2

[@danieldennis9831]

I gof the answer wrong first ... from a stupid arithmetic error. I used the same procedure. That tells me to check my simple math more closely as these simple problems are the ones people pay less attention to.

[@bigm383]

❤😂😀🥂

[@PreMath]

So nice of you. Thank you! Cheers! 😀