1, e is the end of AB, and DE is perpendicular to AB. From these two conditions, we can see that two right-angled triangles ADE and BDE are congruent. According to the nature of the diamond, we know that DB is the bisector of angle ABC, and angle DAB+ angle ABC = 180, so angle ABC=60.

2. The two diagonals of the diamond are perpendicular to each other, so AC=2 times AO. You can prove that AOD and AOB and DEA and DEB are completely congruent four triangles. So DE=AO= root number 3, so AC=2 times (root number 3)

3, the area is equal to the bottom times the height, so AB*DE=2* root number 3=2 times (root number 3).