The bottom surface of straight quadrangular prism ABCD --- a1b1c1d1 with height of 1 is a diamond with area of 2 The area sum of BDD 1B1 is 5, and the bottom edge length of the straight quadrangular prism is calculated

The bottom surface of straight quadrangular prism ABCD --- a1b1c1d1 with height of 1 is a diamond with area of 2 The area sum of BDD 1B1 is 5, and the bottom edge length of the straight quadrangular prism is calculated

Let the diagonal of the bottom diamond be: A, B, a > B
From the meaning of the title: a * 1 + b * 1 = 5,1 / 2Ab = 2
a. B is the two roots of the equation x ^ 2-5x + 4 = 0
a=4,b=1
According to Pythagorean theorem, the length of the bottom edge of a straight quadrangular prism is: √ [(1 / 2) ^ 2 + 2 ^ 2] = √ 17 / 2

Regular prism abcd-a1b1c1d1, side edge length 3, bottom side length 2, e is the midpoint of BC, calculate dihedral angle c1-de-c

The establishment of space rectangular coordinate system to do very fast
The angle c 1mc is the plane angle of dihedral angle

As shown in the figure, in the quadrilateral ABCD, AC = 6, BD = 8 and AC ⊥ BD In this way, we get the quadrilateral anbncndn. (1) prove that the quadrilateral a1b1c1d1 is a rectangle; (2) write out the area of the quadrilateral a1b1c1d1 and a2b2c2d2; (3) write out the area of the quadrilateral anbncndn; (4) find out the perimeter of the quadrilateral a5b5c5d5

(1) It is proved that: ∵ points A1 and D1 are the midpoint of AB and ad respectively, ∵ a1d1 is the median line of △ abd ∵ a1d1 ∥ BD, a1d1 = 12bd, similarly: b1c1 ∥ BD, b1c1 = 12bd ∥ a1d1 ∥ b1c1, a1d1 = b1c1 = 12bd ∥ quadrilateral, a1b1c1d1 is parallelogram. ∵ AC ⊥ BD, AC ∥ A1B1, BD ∥ a1d1, ∥

As shown in the figure, the area of rectangle a1b1c1d1 is 4. Connect the middle points of each side in order to get quadrilateral a2b2c2d2, and then connect the middle points of quadrilateral a2b2c2d2 in order to get quadrilateral a3b3c3d3. And so on, find the area of quadrilateral anbncndn______ ．

∵ the quadrilateral a1b1c1d1 is a rectangle, ∵ A1 = ∵ B1 = ∵ C1 = ∵ D1 = 90 °, A1B1 = c1d1, b1c1 = a1d1; and ∵ the midpoint of each side is A2, B2, C2, D2, ∵ the area of quadrilateral a2b2c2d2 = s △ a1a2d2 + s △ c2d1d2 + s △ c1b2c2 + s △ b1b2a2 = 12 · 12a1d1 · 12a1b1 × 4 = 12 the area of rectangular a1b1c1d1, that is, the area of quadrilateral a2b2c2d2 = 12 the area of rectangular a1b1c1d1; similarly, the quadrilateral a3b3c3d3 = 1 2 area of quadrilateral a2b2c2d2 = 14 area of rectangle a1b1c1d1; and so on, area of quadrilateral anbncndn = 12n − 1 area of rectangle a1b1c1d1 = 42N − 1 = 12n − 3

In quadrilateral ABCD and quadrilateral a1b1c1d1, if AB = A1B1, BC = b1c1, CD = c1d1, Da = d1a1
Then quadrilateral ABCD and quadrilateral a1b1c1d1 are congruent
If AC = a1c1, then the quadrilateral ABCD and the quadrilateral a1b1c1d1 are congruent. Write the process of students' thinking,
(2) Please add another condition (except diagonal) to explain the congruence of the two quadrangles and write down your thinking process
Just answer the second question

Condition ∠ B = ∠ B1
∵ AB = A1B1, ∠ B = B1, BC = b1c1 (edge)
∴△ABC=△A1B1C1
∴AC=A1C1
The following solution is the same as (1)