Find Area of the Yellow shaded triangle when area of Rectangle is 1350 | Important skills explained

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Find Area of the Yellow shaded triangle when area of Rectangle is 1350 | Important skills explained

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[earningtoday]

Sir it was an easy one, normal brain use, total area - area of the three right angle triangles

[abeonthehill]

I calculated the angles of the three white triangles. Then using the two white angles touching each yellow angle a+b+yellow angle =180 degrees ( twice ) the bottom yellow angle a+b+ lowest yellow angle =45 degrees .
I used trigonometry to find the side lengths of the three sides of the yellow triangle as each is a hypotenuse of the three white triangles.
I then used “ Heron’s Rule “ to work out the area of the yellow triangle just as i could not resist comparing to the results of the entire rectangle area -the area of the three white triangles must equal the area of the yellow triangle !
So using the “ Heron’s Rule “ i arrived at as my calculator is limited and rounds off after six decimal places .
Took me about 40 mins with the calculations however, i have enjoyed this one.
Thanks so much for sharing your detailed step-by-step explanations ; i really enjoy your video’s as your method is easy to follow.
Regards……Abe ( UK )

[bengaligolposol]

You can also use the heren's formula .

[rahulpaul]

If we could find the length of hypotones of each are the sides of the yellow triangle and then we can use heron's formula to find the area
i solved in a same way as you did in the video

[anandharamang]

We can take the Trapezium ADFB
Area of Trapezium = 1/2 * 30 * (45+15) = 900, EDF area = 1/2 *12*15= 90, AEB area = 1/2 * 18*45=405, So, required triangle are of EFB= ADFB- ADF-ABE=900-90-405= 405 sq.units.

[yalchingedikgedik]

Very well explained,
Thanks sir .
Thanks PreMath .

[alster]

Easy. I remembered the videos on triangles inscribed in rectangles videos thus making this one pretty straightforward.

[HappyFamilyOnline]

Beautiful presentation👍
Thanks for sharing😊😊

[massimogranzotto]

Difficile per le mie capacità ma la sua ottima spiegazione professore mi ha fatto capire.
Grazie

[prabhagupta]

We can put Pythagorean theorem and find EF EB FB and put herons formula

[GuglielmoArmillei]

I solved it calculating all the hypotenuses of A1, A2, A3 using Pythagorean theorem, that are the A4 side lenghts. Once you have the 3 side lenghts you can calculate A4 by using Heron theorem.

[santiagoarosam]

DF=15 ; AD=1350/45=30 ; EA=30-12=18 →→ We draw a horizontal line through point E and a vertical line through F and the yellow triangle is divided into three triangles with known base and height → Yellow area=(12*15+12*30+15*18 )/2=405
Thanks and best regards

[DDX]

Sir I was very cofused about x because total area was not shown on the thumbnail. When I play the video I suddenly saw the total area then I solved this problem easily myself same as you have told in the vodeo.
Thanks alot...

[philipkudrna]

BC = 30 (as 30*45=1350). This reveals the 3 white (right) triangles have sides 12*15, 30*30 and 18*45. By the area formula a*b/2 the areas of the triangles are 90, 450 and 405 or 945 altogether. Deduct this from 1350 and you get 405 forschte yellow area. (which is actually coincidentally the same are as for the large lower triangle…!)

[theoyanto]

Enjoyable, not too taxing on the grey matter

[theoyanto]

Thank you for this example, kinda thinking inside the box this one :-)

[anjanikumari]

We can apply heron's formula also

[devondevon]

So easy,
405
Since the area of the rectangle is 1350 and one side is 45, then the other side
is 30. 30-12 =18
(18x 45)/2= 405 area of a triangle
(12 x 15)/2= 90 the area of another triangle
(30 x 30)?2 = 450 the area of the other triangle
total area =945
1350-945 = 405 answer

[-biswarooptalukdar]

Sir this sums are for maths olympiad??
Cause I need some sums of olympiad...

[jakkima]

I solved it using an equation and got the following result: A4 = (1350 - AE * FC) / 2 = (1350 - 18 * 30) / 2 = (1350 - 540) / 2 = 810 / 2 = 405.