Summary: 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 a 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 \(r_h=3.0\sqrt{\theta} \).