For a better understanding of the solution/expression provided here please find the diagram of the side view of the pyramid in the attached file.
BC is the base.
.
AP is the height.
. Therefore,

As we can see
is a right triangle where, AC which is the hypotenuse of the triangle is the slant height of the pyramid.
Thus, applying the Pythagoras' Theorem in
we get:

Therefore the slant height of the pyramid is represented by 10.77 m. Thus, Option A is the correct option.