In rectangular ABCD, the diagonal lines AC and BD intersect at O, ∠ AOD = 120 °, BC = 3cm under the root sign. Calculate the length of AC and the area of rectangular ABCD

In rectangular ABCD, the diagonal lines AC and BD intersect at O, ∠ AOD = 120 °, BC = 3cm under the root sign. Calculate the length of AC and the area of rectangular ABCD

Because the triangle ABC is a right triangle, and the angle BAC = 60 degrees
So AC = 2, ab = 1
Rectangular area = 1 ×√ 3 = √ 3

It is known that, as shown in the figure, the diagonal lines AC and BD of rectangle ABCD intersect at point O, AC = 2Ab

It is proved that: ∵ quadrilateral ABCD is a rectangle, ∵ ABC = 90 ° (the four corners of the rectangle are right angles), ∵ in RT △ ABC, AC = 2Ab, ∵ ACB = 30 °, ∵ quadrilateral ABCD is a rectangle, ∵ ob = od = 12bd, OC = OA = 12ac, AC = BD, ∵ Bo = Co, ∵ OBC = ∵ OCB = 30 °, ∵ OBC + ∵ OCB + ∵ B

As shown in Figure 1, in rectangular ABCD, the intersection of two diagonals and point O, ∠ AOD = 120 ° AB = 4
Find the length of the diagonal of a rectangle;
Find the length of BC side
If a straight line passing through point O and perpendicular to BD intersects AD and E, and BC intersects F, it is proved that EF = BF, of = CF
If the rectangle is folded along the line Mn so that the vertices B and D coincide, the length of the broken line Mn is calculated
&Now I have the first question and the second question. Please give me a detailed explanation of the third and fourth questions

(1) Therefore, the diagonal length of the rectangle is 8
(2) BC = radical (8-4 Square) = 4 √ 3
(3) ∠OBF=30°,EF=2OF=2*(1/2BF)=BF
(4) Mn and EF coincide, so the length of Mn is BF = 8 √ 3 / 3

In rectangle ABCD, the intersection of diagonal AC and BD is O, angle AOB = 2, angle AOD, ad = 8, AC =?

∵ - AOB + AOD = 180 ° and ∠ AOB = 2 ∠ AOD
∴∠AOD=60°
∴∠ACD=30°
∴AC=2AD=16