Find the total area of the regular pyramid.

check the picture below.

notice, the base of the "square" pyramid, is a square, and it has 4 triangular faces with a base of 2, and a height of √(10).

so the total surface area is the area of the base plus all 4 triangular faces' areas.

[tex]\bf \stackrel{\textit{squarish base}}{(2\cdot 2)}~~~~+~~~~\stackrel{\textit{4 triangular faces}}{4\left[ \cfrac{1}{2}(2)(\sqrt{10}) \right]}[/tex]