Tipping point

Since the whole system is balanced at the limiting case (when the prism just begins to topple),

Net vertical force is balanced: $mg= N_1 cos(30^o)$

Net horizontal force is balanced: $N_2 = N_1 sin(30^o)$

Thus, we obtain $N_2= \frac{mg}{\sqrt{3}}$ ....................................................................... (1)

Net torque about point A is also zero since the system is in rotational equilibrium.

$mg (\frac{a}{2 \sqrt{3}}-d) = N_2 \frac{d}{\sqrt{3}}$ ......................................................................... (2)

Combining (1) and (2) and solving,we get: $\boxed{d = \frac{a \sqrt{3}}{8}}$ .

Plug in the values to get the answer as $\boxed{0.10825}$

Imgur

Here is a solution , more visual