Correct Answer: 260 cm ²

Solution : Use the formulas:
Area of the slant surface = $\frac{1}{2}×p×l$
Perimeter, $p$ = $4a$
Slant height, $l$ = $\sqrt{(\frac{a}{2})^{2}+h^{2}}$
where $l$ = slant height, $h$ = height, $p$ = perimeter and $a$ = side of square base.
Diagonal of square base $= 10\sqrt2$ cm
Height of the pyramid, $h = 12$ cm
Side of square base, $a = \frac{1}{\sqrt2}×10\sqrt2 = 10$ cm
Perimeter, $p = 4a = 4×10 = 40$ cm
Slant height, $l = \sqrt{(\frac{a}{2})^{2}+h^{2}} = \sqrt{5^{2}+12^{2}} = \sqrt{169} = 13$ cm
Area of the slant surface $= \frac{1}{2}×40×13 = 260$ cm ²
Hence, the correct answer is 260 cm ² .