(4) There is a regular quadrilateral pyramid, with the side length of its base and the side length of its lateral edges both being $a$. Now, it is to be completely wrapped with a square piece of wrapping paper (the paper cannot be cut, but can be folded). Then, the minimum side length of the wrapping paper should be ( ).
(A) $\frac{\sqrt{2}+\sqrt{6}}{2} a$
(B) $(\sqrt{2}+\sqrt{6}) a$
(C) $\frac{1+\sqrt{3}}{2} a$
(D) $(1+\sqrt{3}) a$
(4) When the sides of a regular quadrilateral pyramid are unfolded onto the base, the vertices of the 4 triangular sides form a square, which is the smallest square, with a side length of $\frac{\sqrt{2}+\sqrt{6}}{2} a$. Therefore, the answer is $\mathrm{A}$.