  Using a graphical analysis, we show that for the horizon radius $r_h\gtrsim
4.8\sqrt\theta$, the standard semiclassical Bekenstein-Hawking area law for
noncommutative Schwarzschild black hole exactly holds for all orders of
$\theta$. We also give the corrections to the area law to get the exact nature
of the Bekenstein-Hawking entropy when $r_h<4.8\sqrt\theta$ till the extremal
point $r_h=3.0\sqrt{\theta}$.
