Figure 1, when 0 ≤ t < 1, the area s of the overlapping part is the area of the right-angled trapezoid HCBE;
Fig. 2, when 1 ≤ t < 3, the area s of the overlapping part is the area of the triangular GEF-(the area of the triangular GHI+the area of the triangular KBF), or the area of the trapezoidal HIKJ+the area of the right-angled trapezoidal KBEJ;
Fig. 3, when 3 ≤ t < 4, the area s of the overlapping part is the area of the isosceles trapezoid HIFE;
Fig. 4. When 4 ≤ t < 6, the area s of the overlapping part is the area of the triangle GFE.
The green line in the figure indicates the starting and ending position, and the red line indicates the general situation. So you can understand. If you have any questions, write down the results and keep asking.
In the diagram 1 The base BE of the trapezoid is 3+t, and the height BC is the root of 2. 3? , upper and lower HC = 2-(1-t) =1+t.
(If the other side of the red triangle of HC extends to R and the rightmost green line extends to Q, the triangle GHR is similar to the triangle GEF, and the similarity ratio can be obtained from the height ratio of 1: 3, so HR=2, CQ= 1, RQ=t, CR= 1-t, so HC = HR-Cr =
In fig. 2, the area of the triangular GEF is 9 times of the root number 3, the area of the triangular GHI is the root number 3, and the area of the triangular KBF is 1/2[(3-t)* root number 3 times (3-t)]. Therefore, S=(-? (root number 3)/2)×t square +(3? Bigen 3)t+？ (7th root number 3)/2.
In fig. 3, the lower base EF of the isosceles trapezoid is 6-2(t-3)= 12-2t, and the height BC is 2. , upper and lower HI=( 12-2t)-4=8-2t,
(when the intersection h is HT vertical EF and intersection t, ET=2 and HI=EF-2ET are obtained by multiplying HT=2 by root number 3, ∠ het = 60).
So, S=-4 at this time? Multiply the root 3t+20 times the root? 3。
In fig. 4, the triangle GEF is an equilateral triangle with a side length of 6-2(t-3)= 12-2t and a direction of (6-t)* root number of 3. Therefore, S=? The root number 3 times the square of t -( 12 times the root number 3)t+36 times the root number 3.