Can you find area of the Blue shaded region? | (Think outside the Box) |
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- เผยแพร่เมื่อ 4 ต.ค. 2024
- Learn how to think outside the box to find the area of the Blue shaded region. Important Geometry and Algebra skills are also explained: area of the triangle formula; similar Triangles with same area. Step-by-step tutorial by PreMath.com
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Can you find area of the Blue shaded region? | (Think outside the Box) | #math #maths | #geometry
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Âmzing! Thank you professor.
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You are very welcome!
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Great problem
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Thank you. Appreciate the new insight!
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Simply great, Sir!
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Amazing!
Think out of box is take advantage of the extreme case, 8×4 rightangled triangle, the area of this triangle 4x8/2=16 is the answer.
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Very good.
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excellent Prof! 👌
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1/ Label CE= x and AD = y
A1= Area of the triangle ADF , A2= area of EFB, and A3= area of the quadrilateral CDFE
We have:
Area of trangle CAE= 1/2 x.(8+y)=A1+A3
or 4x+ xy/2= A1+ A3 (1)
Area of triangle CDB= 1/2 . 8.(x+4)=4x +16 = A2+A3 (2)
(2)-(1) -> A2-A1= 16- xy/2
Because the height from F to the base AD = x/2
so area of the triangle ADF =xy/4
-> A2-A1 = 16-2A1
--> A2+A1= 16 sq units😅😅😅
Excellent!
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START HERE IT'S GOOD START...
Say EC is some value x. Thus area of BDC is (8*(4+x)/2) and similarly area of AEC is equal to that but for some value AD = y. So that the area of AEC is equal to x(8+y)/2 = (8*(4+x)/2) so that y=32/x. Using similarity, the height of ADF is x/2 if AD is the base. So area of ADF is (32/x) * (x/2) = 16
Cogito, ergo sum , "I think therefore I am". ..Outside the Box not so much! 🙂
😀
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72 Sq unit ?
The area is 16 units square. I kind of disagree with the title, "think outside the box". I think that it is a brain teaser that test out how easily one's intuition fails you. I mean due to the vertical angles being collinear, the bases of both triangles are equal, correct??? And because one of the sides of the larger triangle forms a vertical angle and is collinear with the two A1 triangles, we already know that the area is the one half of the larger side and the smaller side. I hope that that is a sufficient takeaway.
Thanks for the feedback ❤️