Find area of the Blue shaded region | Two squares | Important Geometry skills explained

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Find area of the Blue shaded region | Two squares | Important Geometry skills explained

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[orangeankylosaur]

I really enjoy your posts. Every day, I pick out a problem to solve. My father was an engineer. I'm only sorry he's not alive to see your posts, because I know he would have enjoyed them, too!

[vara]

Every problem you solve is interesting. I look forward to viewing your videos.

[johnnyragadoo]

I solved it somewhat differently. The slope of the diagonal is 9/15, so the height of the smaller triangle is 6*9/15. Nice challenge. Many thanks!

[procash]

Super ji. I am always amazed at the way you describe & explain the solution. No competition to you from anyone

[claudiaschartmann]

😊 It took me 3 minutes to find the correct answer . Thank you for having improved my math abilities , Sir .

[MrPaulc]

A better method than mine, thank you. I went for AE=sqrt(306) (or 3root34). To find the length of the diagonal in the left square I took 2/5 of sqrt(306). This gave the the length of x via Pythagoras, ((2/5)*sqrt(306))^2 - 36 = x^2. I then multiplied (1/2)x * 6 and subtracted from 36. Your way was cleaner though and I overcomplicated it.

[Waldlaeufer]

9 : 15 = x : 6
x = 54/15 = 3.6
A = 1/2(6 + (6 - 3.6)(6) = 1/2(8.4)(6) = 4.2 * 6 = 25.2 square units

[alster]

Wow, that was amazing. Keep it up, Premath

[gaylespencer]

Could also integrate (9/15)x over 0 to 2, as .6(36^2/2), then subtract that from the area of the small square.

[tanaysingh]

Very nice idea no one can judge you hardwork making these things keep it up

[BabitaKumari-gdmh]

It takes 58.98 hours to find the correct ans thanku

[towguy]

To do the math in my head, I looked at the larger similar triangle and added 6+9=15:9, so a ration of 5:3. smaller triangle has a base of 6 (or 5+1) so give it a height of 3 for 5 and 3/5 for 1 to equal 3 3/5. 1/2 BH is 3 * 3 3/5 = 9 9/5 = 10 4/5. smaller square is 6^2=36. Shaded area is 36 - 10 - 4/5, or 25 1/5 (25.2).

[devondevon]

My approach using trigonometry:
Sides 15 (9+6) and 9, and angle 90 degrees (SAS), which gives an angle of 30.94 degrees. Then 30.94 degrees, 90 degrees, and side 6 (ASA) give a side of 3.6. Hence the length of the smallest shaded side is 2.4 (6-3.6).
Since it is a trapezoid, the formulae (2.4 +6)/2* 6 = 8.4/2* 6 = 4.2* 6 = 25.2 Answe

[dhrubajyotidaityari]

Area under the diagonal ½.9.15=135/2
Let x= the line which divides this triangle. Hence
135/2=½.6x+½.9(x+9)
x=18/5
Left side lower triangle ½.6.18/5=54/5
Shaded part=36—54/5=&c

[theoyanto]

Whoo, I did it, took me a few minutes to see it but great problem, thank you once again 👍🏻

[tricky]

126/5 unit square is the answer, thank you sir 🙏🙏

[spiderjump]

By similar triangles, the height of smaller triangle formed by diagonal line = 2/5x9=18/5
Area of triangle =1/2x6x18/5=54/5
Area of shaded part= 36 — 54/5

[Greengales]

Same concept similar triangles except i look at the 9 square length and used (9-x)/9 and solved it still.

[liliyakaloyanova]

The verticals of the white triangles(which are similar) have proportion the same as other their sides x1/x2 = 9/6=3/2 x1= 3. x2/ 2 x1+x2=9 3.x2/2+x2=9 5.x2=18 x2=18/5 =3, 6
so the little base side of the blue trapezoid a= 9-3 - 3, 6=2, 4, big base side is 6
Blue Area A= (a+b).h/2= (2, 4+6).6/2= 8, 4.3 =25, 2

[kennethstevenson]

(15x9)/2 - 18 -24.3 = 25.2 square units. I did the work but it was erased, I didn't want to type it in again. The height of the upper triangle is 27/5 units using similar triangles, its area is 24.3 square units. 18 square units is the area of the rectangle missing from the upper left of the figure.