S(ABCD)= 1/2 AC*BD=96

So BD = 12.

Let AC and BD meet O, then OA = 8 and OD = 6.

From Pythagorean Theorem: AD = 10

That is, the length of the diamond is 10.

2. Diagonal lines of diamonds are 12cm and 16cm respectively.

(The method is the same as 1 topic): The length of the diamond is 10.

The rhombic area s =1/2 *12 *16 = 96.

S = side length * height

So the height is 96/ 10 = 9.6.

3 ABCD is a parallelogram.

Therefore ∠ A+∠ B = 180.

∠ ABF = 1/2 ∠ B，∠ EAB = 1/2 ∠ A

Therefore ∠ ABF+∠ EAB = 90.

Let AE and BF meet at O.

Then ∠ AOB = 90, that is, AE⊥BF.

∠ ABF =∠ FBE =∠ AFB。

So AB = AF, and similarly AB = BE.

So af = be, AF//BE

So ABEF is a parallelogram

AE⊥BF again.

So ABEF is a diamond.