Given, perimeter of a pyramid is $x,$ so slant height is $\dfrac{x}{2}.$
Lateral Surface Area of a pyramid
$= \dfrac{1}{2} \times \text{perimeter}\times \text{slant height}$
$= \dfrac{1}{2} \times x \times \dfrac{x}{2}$
$= 0.25 x^{2}$
so option D is correct .