Third-party libraries (TPLs) are extensively utilized by developers to expedite the software development process and incorporate external functionalities. Nevertheless, insecure TPL reuse can lead to significant security risks. Existing methods are employed to determine the presence of TPL code in the target binary. Existing methods, which involve extracting strings or conducting function matching, are employed to determine the presence of TPL code in the target binary. However, these methods often yield unsatisfactory results due to the recurrence of strings and the presence of numerous similar non-homologous functions. Additionally, they struggle to identify specific pieces of reused code in the target binary, complicating the detection of complex reuse relationships and impeding downstream tasks. In this paper, we observe that TPL reuse typically involves not just isolated functions but also areas encompassing several adjacent functions on the Function Call Graph (FCG). We introduce LibAM, a novel Area Matching framework that connects isolated functions into function areas on FCG and detects TPLs by comparing the similarity of these function areas. Furthermore, LibAM is the first approach capable of detecting the exact reuse areas on FCG and offering substantial benefits for downstream tasks. Experimental results demonstrate that LibAM outperforms all existing TPL detection methods and provides interpretable evidence for TPL detection results by identifying exact reuse areas. We also evaluate LibAM's accuracy on large-scale, real-world binaries in IoT firmware and generate a list of potential vulnerabilities for these devices. Last but not least, by analyzing the detection results of IoT firmware, we make several interesting findings, such as different target binaries always tend to reuse the same code area of TPL.