【Haichuan Teahouse】Brain-teasing Series: The midpoint – is it the key point, or still the midpoint?
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Title: As shown in the figure, the side length of square ABCD is 2 cm. Points E and F are the midpoints of sides CD and BC respectively. Connect these points; find the area of the shaded region.
I’ve forgotten it all. I don’t know how to do it
By using this right angle (which is not difficult to prove), it can be determined that the shorter leg of the shaded triangle is \(\frac{\sqrt{5}}{5}\); the length of the other side couldn’t be determined……
The areas of the following three triangles are all the same, equal to 1/3. The area of the red triangle above can also be determined using similar triangles and is 1/5. The area of the shaded region is equal to 1 – (1/3 – 1/3 – 1/5) = 2/15. That’s all!