Step 1: Use a direct formula instead of finding the radius separately.
For a circle inscribed in a square of side $a$, the area of the circle can be written straight away as \[ \text{Area} = \frac{\pi}{4} a^2 \] since the diameter equals the side, and $r = a/2$ folded into the area formula gives this neat form.
Step 2: Substitute the given side length.
Here $a = 6$ cm, so \[ \text{Area} = \frac{\pi}{4} \times 6^2 = \frac{\pi}{4} \times 36 \]
Step 3: Simplify.
\[ \text{Area} = 9\pi \text{ cm}^2 \]
Step 4: Confirm.
This matches what we would get by first finding the radius as 3 cm and then applying $\pi r^2$, but it skips that middle step.
\[ \boxed{9\pi \text{ cm}^2} \]