The volume of a regular pyramid is 2 / 3 of the root sign, and the minimum surface area is obtained

The volume of a regular pyramid is 2 / 3 of the root sign, and the minimum surface area is obtained

Let the side length of the bottom square be a and the height be H
Then 1 / 3A ^ 2H = radical 2 / 3
That is, a ^ 2H = root 2
The height of the side is the root [H ^ 2 + (1 / 2a) ^ 2]
The surface area of a regular pyramid is a ^ 2 + (1 / 2) a radical [H ^ 2 + (1 / 2a) ^ 2] * 4
=A ^ 2 + 2A radical [H ^ 2 + (1 / 2a) ^ 2]
=A ^ 2 + radical (8 + A ^ 6)
A cannot be zero, it seems that there is no minimum value