This is a 5th grade math problem: Knowing the area of a part of a figure inside a rectangle, find its overall area! This question is quite difficult, and the entry point is very narrow! If the method is not right, it will not help if you want to break your head; If the method is correct, it is easy to solve and the answer can be calculated orally. It's really so-called: those who know will count orally, and those who are difficult will be in vain! Judging from the answering situation, it is very unsatisfactory, almost no one does it right, and Xueba is no exception!
Question 477 of Bei Xiao's question set: As shown in Figure 1,
The point E is a point inside the rectangular ABCD, the BCE is an equilateral triangle with an area of 8, and the area of the shaded triangle BDE is 3.
Title or entry point: BCE is an equilateral triangle i.e. be=ce!
Analysis 1: Connect to AE! See Figure 2
From BE=BC, we can know that S CDE=S ABE=1 4S rectangular ABCD. S BDE+S BCD=S BCE+S CDE, that is, 3+1 2S rectangular = 8+1 4S rectangular ABCD. Thus the s rectangular abcd = 5 4 = 20.
Analysis 2: Connect AC, remember that the midpoint between it and BD, that is, the center of the rectangle, is O! As shown in Figure 3
If you connect the OE, you can know the OE CD by be=CE. s ode=s oce, thus s shades bde=s quadrilateral boce. Therefore, s boc = s bce-s quadrilateral boce = 8-3 = 5. Therefore S rectangular ABCD=4S BOC=20.
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