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As shown in the figure below, E is a point on a rectangular ab, the area of δade is 40 square centimeters, the area of δcdo is 45 square centimeters, and the area of rectangular ABCD is how many square centimeters?
In trapezoidal BCDE, ΔBDE and ΔBCE are the same height and equal in area. If both subtract ΔBEO, then the ΔDEO and ΔBCO areas are equal.
Then use letters to represent the area of the three unknown triangles in the figure, as shown in the following figure
Since the sum of the areas of δade + δbeo + δbco is half of the area of rectangular ABCD; The sum of the areas of ΔEDO + ΔCDO is also half the area of a rectangular ABCD.
From this the equation is as follows:
40+y+x=x+45
The solution is y=5, as shown in the following figure:
BEO and ΔCDO form an hourglass model, and the area ratio of the two is 5:45=1:9, so the ratio of the corresponding sides of the two triangles is 1:3.
It can be seen that EO:CO=1:3, and ΔBEO and ΔBCO are contour models, and the area ratio of the two is also 1:3.
Therefore, the area of δBCO is: 5 3 = 15 (square centimeters).
So, the area of a rectangular ABCD is: (15+45) 2=120 (square centimeters).
Elementary Mathematics