△ABC is not necessarily isosceles. However, since DEGF is a square, DE is parallel to AB. Therefore, by the intercept theorem, △ABC ~ △DEC. So, if h is the height of △ABC, we have (h − √36) / √36 = h / √676 ⇒ h = 39/5 and the area of the green region is ½ (26) 39/5 − 36 = 327/5 cm².
The way I did it is: Side of the red square = sqrt(676)=26 Side of the blue square = sqrt(36)=6 Base of the green triangle = (26-6)/2=10 If we combine the 2 green triangles, we get a big green triangle similar to the small one in the top The base of the big combined green triangle =20, the height is=6 The base of the small green triangle =6,the height =x x/6 = 6/20 x=36/20=9/5 Area of the big combined green triangle =0.5*20*6=60 Area of the small green triangle =0.5*6*9/5=27/5=5.4 Total green area =60+5.4=65.4 square units
By similarities pink quadrangle is a square, so AB is the same length as all the other sides. Area of pink square = sₚ² 676 = sₚ² sₚ = √676 = √(4)(169) = 2(13) = 26 Area of blue square = sᵤ² 36 = sᵤ² sᵤ = √36 = 6 Let D be a point on AB where CD is perpendicular to AB and bisects the blue square, E be the point where the blue square intersects CB, and F be the bottom right corner of the blue square. ∆CDB is similar to ∆EFB, so CD is similarly proportional to EF as DB is to FB. CD/EF = DB/FB CD/6 = 13/(13 - 3) CD = (13/10)/6 = 78/10 = 7.8 Green area = Area of ∆ABC - 36 A = bh/2 - 36 A = 26(7.8)/2 - 36 A = 13(7.8) - 36 A = 101.4 - 36 = 65.4
Before video: pink square sides are 26 and blue square side are 6. The two largest green triangles are (13-3)*6, so 10 by 6. Don't bother halving the base because there are two of them, so two equal green triangles = area of 60. Half of the top triangle is similar to one of the larger green triangles. Therefore, 3/x = 10/6. Cross multiply for 10x = 18, so x = 1.8. 1.8*3=5.4. 60+5.4=65.4cm^2. Just watched the video. This one didn't stretch me. I did it broadly the same way, but calculated the smaller triangles separately. Thank you. You are an education. Your explanations contain far more clarity than I see on other maths channels.
No peeking, but I did use a calculator for the square root of 676. The side of the pink square is 26 cm. Therefore each of the lateral green triangles is 10 cm wide and 6 cm tall, and the two together total of 60 square cm. The uppermost small green triangle is made of two triangles each similar to lateral green triangles. Each of these will be 3 cm wide and (6/10)(3) cm tall, and the two together will be (3)(18/10), or a total of 5.4 square cm. So the total green area is 60 + 5.4 = 65.4 square cm. Coraggio. 🤠
ABDE is a square AB,=BD=DE=EA=√676=26cm Lenge of the small square=√36=6cm Small triangle is CFG Angle CFG ~ CAB (AA) h1/h1+6=6/26 26h1=6(h1+6) 26h1=6h1+36 26h1-6h1=36 20h1=36 h1=36/20=9/5cm h=h1+6=9/5+6=(9+30)/5 h=39/5=7.8cmcm So: Area of the green shaded region=1/2(26)(7.8)-36=65.4cm^2.thanks ❤❤❤
Good morning from Brazil. I really like your channel, but I would like there to be more diversity in the topics covered, that is, more different subjects, such as equations, potentiation, etc.
Similar triangles help with estimating distance. Using thumb and switch closing eyes focused on distant object and multiplied by ten a known width like a car. Cyclops had a distinct disadvantage! 🙂
This one was so simple that you can do it in your head. Also...too many find the area or length of geometry problems. Can you try something else please !!
How do we determine that the blue square is located symmetrically? I abandoned my attempt to solve this problem because I realised I couldn't demonstrate symmetry, and then the proof skipped this step...
Love it!!!!!!!!!!!
Thank you so much ❤️
△ABC is not necessarily isosceles. However, since DEGF is a square, DE is parallel to AB. Therefore, by the intercept theorem, △ABC ~ △DEC.
So, if h is the height of △ABC, we have (h − √36) / √36 = h / √676 ⇒ h = 39/5 and the area of the green region is ½ (26) 39/5 − 36 = 327/5 cm².
Thanks ❤️
The way I did it is:
Side of the red square = sqrt(676)=26
Side of the blue square = sqrt(36)=6
Base of the green triangle = (26-6)/2=10
If we combine the 2 green triangles, we get a big green triangle similar to the small one in the top
The base of the big combined green triangle =20, the height is=6
The base of the small green triangle =6,the height =x
x/6 = 6/20
x=36/20=9/5
Area of the big combined green triangle =0.5*20*6=60
Area of the small green triangle =0.5*6*9/5=27/5=5.4
Total green area =60+5.4=65.4 square units
Thanks ❤️
This problem is simpler than usual.
Thanks ❤️
Thanks Sir
That’s very useful method
Glades
Found arctan of angle CBA, then used that to find height of triangle.
Thanks ❤️
By similarities pink quadrangle is a square, so AB is the same length as all the other sides.
Area of pink square = sₚ²
676 = sₚ²
sₚ = √676 = √(4)(169) = 2(13) = 26
Area of blue square = sᵤ²
36 = sᵤ²
sᵤ = √36 = 6
Let D be a point on AB where CD is perpendicular to AB and bisects the blue square, E be the point where the blue square intersects CB, and F be the bottom right corner of the blue square. ∆CDB is similar to ∆EFB, so CD is similarly proportional to EF as DB is to FB.
CD/EF = DB/FB
CD/6 = 13/(13 - 3)
CD = (13/10)/6 = 78/10 = 7.8
Green area = Area of ∆ABC - 36
A = bh/2 - 36
A = 26(7.8)/2 - 36
A = 13(7.8) - 36
A = 101.4 - 36 = 65.4
Before video: pink square sides are 26 and blue square side are 6.
The two largest green triangles are (13-3)*6, so 10 by 6. Don't bother halving the base because there are two of them, so two equal green triangles = area of 60.
Half of the top triangle is similar to one of the larger green triangles.
Therefore, 3/x = 10/6.
Cross multiply for 10x = 18, so x = 1.8.
1.8*3=5.4.
60+5.4=65.4cm^2.
Just watched the video. This one didn't stretch me. I did it broadly the same way, but calculated the smaller triangles separately.
Thank you. You are an education. Your explanations contain far more clarity than I see on other maths channels.
Super!
Thanks ❤️🌹
No peeking, but I did use a calculator for the square root of 676.
The side of the pink square is 26 cm. Therefore each of the lateral green triangles is 10 cm wide and 6 cm tall, and the two together total of 60 square cm.
The uppermost small green triangle is made of two triangles each similar to lateral green triangles. Each of these will be 3 cm wide and (6/10)(3) cm tall, and the two together will be (3)(18/10), or a total of 5.4 square cm. So the total green area is 60 + 5.4 = 65.4 square cm.
Coraggio. 🤠
Thanks ❤️
Thanks, Professor, very succinct!❤
Thank you so much ❤️
ABDE is a square
AB,=BD=DE=EA=√676=26cm
Lenge of the small square=√36=6cm
Small triangle is CFG
Angle CFG ~ CAB (AA)
h1/h1+6=6/26
26h1=6(h1+6)
26h1=6h1+36
26h1-6h1=36
20h1=36
h1=36/20=9/5cm
h=h1+6=9/5+6=(9+30)/5
h=39/5=7.8cmcm
So: Area of the green shaded region=1/2(26)(7.8)-36=65.4cm^2.thanks ❤❤❤
Thanks ❤️
Good morning from Brazil. I really like your channel, but I would like there to be more diversity in the topics covered, that is, more different subjects, such as equations, potentiation, etc.
Good suggestion!
Thanks ❤️🇺🇸
Similar triangles help with estimating distance. Using thumb and switch closing eyes focused on distant object and multiplied by ten a known width like a car. Cyclops had a distinct disadvantage! 🙂
Thanks for sharing!😀
S=65,4 cm²
Yay! I solved the problem.
Wow!
Thanks ❤️
Answer: 65, 4 cm^2
x/13 = 6/10
x = 78/10
x = 7,8 cm
(7,8 * 26) / 2 = 202,8 / 2 = 101,4
101,4 - 36 = 65,4
Thanks ❤️
How did you know that AC=CB ?
Symmetry
Nice! tan(δ) = 3/5 = k/3 → k = 9/5 → (1/5)(3(169) - 180) = 327/5
Thanks ❤️
very nice video❤❤❤
Thank you so much ❤️
tg(A)=0,6, CQ=13*tg(A)=13*0,6=7,8. S=26*7.8/2-36=65,4
Thank you so much ❤️
I due triangoli laterali hanno area (6*10/2)*2=60..il triangolo in alto ha A=6*1,8/2=5,4...totale 65,4
Super!
Thank you so much ❤️
13/ |cq| = 10/6=5/3 so |cq|= 39/5 etc.
This one was so simple that you can do it in your head.
Also...too many find the area or length of geometry problems. Can you try something else please !!
Thanks ❤️
How do we determine that the blue square is located symmetrically? I abandoned my attempt to solve this problem because I realised I couldn't demonstrate symmetry, and then the proof skipped this step...
This problem can be solved without assuming that there is symmetry 😉
Is it given that the blue square is in the exact center of top side of pink square?
Symmetry!
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Got the answer on the first try.
Great!
Thanks ❤️
Coincidentally I just finished working on a previous problem from one of your videos lol
Great!
Thanks ❤️
The side length of the pink square is 26 cm.
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Easy
Thanks ❤️
65.4
Thanks ❤️