In addition to B-EFB 1, there are two pyramids, B 1-A 1C 1FE and B-EFCA.

Then find the volumes of B 1-A 1C 1FE and B-EFCA.

The plane height from B 1 to A 1C 1FE is √3a/2, and the area of A 1C 1FE is A 2/2.

Similarly, the height from B to EFCA is √3a/2, and the area of EFCA is A 2/2.

Then the volume of these two parts is1/3 * 2 * √ 3a/2 * a2/2 = (√ 3/6) * a3.

The volume of triangular prism is: (√ 3/4) * a 2 * a = (√ 3/4) * a 3.

Then the volume of B-EFB 1 = (√ 3/4) * a3-(√ 3/6) * a3 = (√ 3/12) a3.