【Haichuan Teahouse】Brain-teasing Series: Some conditions are redundant
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Title: As shown in the figure, quadrilateral ABCD is a square. Point E is located outside the square. Lines AE, BE, CE, and DE are drawn. Given that the side length of the square is 10, CE = 6, and DE = 8, find the area of the shaded region.
Those 2 points probably don’t form a right angle
For two triangles with a base of 10, the total height is 10 and the area is 50
It’s indeed a right angle: hypotenuse 6, legs 8 and 10!
The area is 50. The bases of the two shaded triangles are both 10, and the sum of their heights is also 10
Well, sometimes too many conditions can be distracting……
This condition is a bonus condition and not necessary
As long as the distribution range of point E falls within the extension lines of lines AB and CD, this area remains a constant value