【Haichuan Teahouse】Brain-Training Series: Daily Practice for Middle School Students
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The side length of the square is 5, DE = DC, and the area of triangle ADE is 7.5. Find the area of the shaded region
This post was last edited by zqwqiwu123 on 2021-10-27 at 10:48. . .
The height of triangle AED is 3; it is a special triangle, following the ratio 3-4-5. Once these dimensions are known, the area of the shaded region equals the area of the square minus the areas of the two triangles and one trapezoid. Solution complete
Finding the height is clever; dividing it into several parts makes the calculation even more clever
It is said that this represents the daily life of junior high school students in a major province in the Central Plains
Smart – the area of two triangles minus the area of one triangle (half the area of a square), and the answer is 5
This post was last edited by wjl7212 on 2021-10-27 at 16:35: 1) Connect to BE. 2) Draw a auxiliary line FG through point E such that FG is perpendicular to BC. 3) It is given that the area of triangle ABC, S1, is 12.5, the area of triangle ADE, S2, is 7.5, and AD = 5. It can be concluded that EF=3, EG=2, BG=1; the area of triangle BCE is S3=5, and the area of triangle ABE is S4=2.5. 4) Therefore, the area of the shadow = S1 – S3 – S4 = 5. Answer: The shaded area is 5