Is there a formula to calculate ground distance traveled given rate of climb and true airspeed?
You need ground speed not TAS. GS is affected by the head- or tail-wind components.

Assuming in your example GS is 75 knots, then just check how long it takes to change altitude.

11,200 ft at 1,250 ft/min takes 8.96 minutes, or 0.1493 hours.

At a speed of 75 knots, that's 11.2 NM.

$$\frac{\text{altitude change (ft)}}{\text{rate of climb (ft/min)}\cdot60}\cdot\text{ground speed (knots)}$$



Since the density of air changes during a climb/descent, it affects the rate of climb/descent. Fancy planes have green bananas or similar indications on the navigation display to show where you'll reach the target altitude (it updates in real-time).

The green arc is that green banana (altitude range arc).