Answer: (full score of this question 12) There are two small questions in this question, 1 full score of the small question (6 points) and the full score of the second small question (6 points).

Solution: (1) Because in the regular quadrangular prism ABCD-a1b1c1d1,

The bottom ABCD is rectangular, AB= 1, BC=2, AA 1=2, and E is the midpoint of the side BB 1.

So s △ a 1ed = 12x2 = 2,

So VA? A 1ED=VE？ a 1AD = 13S△a 1ED？ AB=23。

(2) take the midpoint f of CC 1 and connect DF, b1f. ..

Because DF∑AE, the angle between DF and B 1D is equal to the angle between AE and b1d.

In △B 1DF，B 1d = 7，DF=2，B 1f = 3，

So cos ∠ b1df = df2+db12? B 1F22DF？ DB 1=3 14 14，

So the angle formed by AE and B 1D is arccos 3 14 14.