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Area of a rhombus or kite



Suppose we have a ten inch line segment. Draw two isosceles triangles with legs of 3inches such that each begin at the end of the line and their hypotenuse is opposite of the base line. Extend the hypotenuse lines such that they cross above the middle of the line segment. Draw a line from the height of each triangle to the bottom end of the other triangle (the acute angle). At the top a four-sided shape is formed. What is the area of this shape?  Solve it without calculus. 

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I spent way too much time trying to figure out the calculus ban. Like there a catch and it should be obvious at some point. If there was a catch I didn't see it.


The point coordinates are
A: (5,5) B: (0,0) C: (10,0) D: (3,3) E: (7,3) F: (5, 15/7) G: (3,0) H: (7,0) I: (3,9/7) J: (7,9/7)


ABC = 25
FBC = 75/7
BDI = ECJ = BDG - BIG = 9/2 - (1/2)(27/7) = 18/7
DFI = FEJ = (1/2)(2)(3-9/7) = 12/7

AEFD = ABC - (FCB + 2xBDI + 2xDFI) = 40/7 ~ 5.71428


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