As shown in the figure, in the diamond ABCD, ab = 2, ∠ C = 60 °, the diamond ABCD rolls to the right on the straight line l without sliding. Each rotation of 60 ° around a vertex is called an operation. After 36 such operations, the total length of the path that the diamond center o passes through is (the result retains π)______ ．

The sum of arc length of the first and second rotation is 60 π × 3180 + 60 π × 3180 = 2 × 60 π × 3180, the arc length of the third rotation is 60 π × 1180, ∵ 36 △ 3 = 12, so the total path length of the center O is 12 (2 × 60 π × 3180 + 60 π × 1180), = (83 + 4) π

If the vertices a and B of rectangle ABCD are on the number axis, the number corresponding to point a is - 2, and the number corresponding to point B is root 5, then the length of CD is ()

It is known that ab = radical 5 - (- 2) = radical 5 + 2
Because the rectangle ABCD has: CD = ab
So easy to get: CD = root 5 + 2

It is known that points a (1,2) and B (5,6) in the graph. The line CD of length 1 moves on the x-axis. When the perimeter of the quadrilateral ABCD is the smallest, the coordinate of point D is

Let me tell you how to solve the problem
Do a, B about X axis symmetry point A1, B1, take e (2,2), f (4,6), connect EB1, FA1, and X axis intersection is C, D coordinates. Specific value you should be able to find out

Given the point a (1,2) point B (5,6), the line CD with length 1 moves on the x-axis, when the circumference of the quadrilateral ABCD is the smallest
Given the point a (1,2) and point B (5,6), the segment CD with length of 1 moves on the x-axis. When the perimeter of the quadrilateral ABCD is the smallest, the coordinates of point D are the same

Let C be (a, 0), then d be (a + 1,0)
In the quadrilateral ABCD, the length of AB is not changed, so is the length of CD
What changes is the length of AD and BC
∵AC²=(a-1)²+4 BD²=(a-5)²+36
∴AC²+BD²≥2AC*BD
If and only if AC = BD, there is a minimum
That is, when a & # 178; - 2A + 5 = A & # 178; - 10A + 61, AD & # 178; + BC & # 178; is the smallest,
In this case, 8A = 56, a = 7
So when a = 7, AD + BC is the smallest
Therefore, because AB and CD are invariable, we can know that when a = 7, the perimeter of quadrilateral ABCD is the smallest
At this time, the coordinate of point D is (8,0)

In the quadrilateral ABCD, the bisector of angle a is divided into two segments with the length of 4cm and 5cm, then the perimeter of quadrilateral ABCD is?

Two answers
1）28cm
2)26cm

As shown in the figure, in the quadrilateral ABCD, ab ‖ CD, ∠ B = ∠ D, BC = 6, ab = 3, find the perimeter of the quadrilateral ABCD

Solution 1: ∵ ab ∥ CD ∥ B + ∠ C = 180 °, and ∵ B = ∠ D, ∵ C + ∠ d = 180 °, and ∥ ad ∥ BC shows that ABCD is a parallelogram, ∥ AB = CD = 3, BC = ad = 6, ∥ the perimeter of quadrilateral ABCD = 2 × 6 + 2 × 3 = 18; solution 2: connect AC, ∵ ab ∥ CD, ∥ BAC = ∠ DCA, and ∥ B = ∠ D, AC = Ca, ≌ ABC ≌ CDA, ≌ AB = CD = 3, BC = ad = 6, ∥ the perimeter of quadrilateral ABCD = 2 × 6 + 2 × Solution 3: connect BD, ∵ ab ∥ CD ∥ abd = ∥ CDB, and ∵ ABC = ∥ CDA, ∥ CBD = ∥ ADB, ∥ ad ∥ BC, that is, ABCD is a parallelogram, ∥ AB = CD = 3, BC = ad = 6 (5 points) ∥ the perimeter of quadrilateral ABCD = 2 × 6 + 2 × 3 = 18

It is known that quadrilateral ABCD is similar to quadrilateral a'b'c'd ', and ab: BC: CD: Da = 20:15:9:8, the perimeter of quadrilateral a'b'c'd' is 26,
Find the length of each side of quadrilateral a'b'c'd '

.
Because the two polygons are similar, so
A'B':B'C':C'D':D'A'=20:15;9;8
A'B'=26X20/52=10
B'C'=26X15/52=7.5
C'D'=26X9/52=4.5
D'A'=26X8/52=4

The vertex coordinates of the quadrilateral are a (- 1,4), B (2,2), C (4, - 1), D (- 2, - 2), and the area of the quadrilateral ABCD is calculated
Known answer is 20, find the process

The vertex coordinates of the quadrilateral are a (- 1,4), B (2,2), C (4, - 1), D (- 2, - 2), and the area of the quadrilateral ABCD is calculated
AB = root 13
BC = root 13
CD = root 37
Da = root 37
AC vertical BD
AC = 5 radical 2
BD = 4 radical 2
Area of quadrilateral ABCD = 0.5 * ac * BD = 20

The four vertex coordinates of the quadrilateral ABCD are a (1,2) B (4,3) C (3,6) d (0,5). Judge whether the quadrilateral is a square and explain the reason

Vector AB = (3,1), vector BC = (- 1,3), vector CD = (- 3, - 1), vector Da = (1, - 3), vector AB = vector BC = vector CD = vector Da = root 10, so quadrilateral ABCD is diamond. And because vector AB * vector ad = vector AB * vector ad * cosa, namely (3,1) * (- 1,3) = root 10 * root 10 * cosa = 0, cosa = 0, so a = 90 degree, So the quadrangle is square. If there is something unclear, I hope it can help you!

It is known that the four vertices of the quadrilateral ABCD are a (4,5), B (1,1), C (5,3) d, (8,7), the line L passes through P (- 1, - 2), and the area of the quadrilateral ABCD is known
It is known that the four vertices of the quadrilateral ABCD are a (4,5), B (1,1), C (5,3) d, (8,7). The line L passes through P (- 1, - 2) and bisects the area of the quadrilateral ABCD. The equation of L is obtained

ABCD is obviously a parallelogram. The AB vector is equal to the DC vector
Bisecting the area of a parallelogram goes through the center of the parallelogram
That is, the straight line passes through the point (4.5,4)
Find the straight line of point (4.5,4) and (- 1, - 2)