The next-generation video coding standard Versatile Video Coding (VVC) adopts Multiple Transform Selection (MTS) to the transform module, improving coding efficiency at the expense of high computational complexity. Compared to High Efficiency Video Coding (HEVC), VVC supports larger sizes and extends the transform types to Discrete Cosine Transform (DCT)-II, Discrete Sine Transform (DST)-VII, and DCT-VIII. This paper presents an area-efficient unified architecture for VVC to implement the transform module more efficiently. To reduce the area consumption, we propose an optimized calculation scheme for general transformation where the transform matrix is decomposed into two simpler matrices named the Low-value matrix and the Error matrix. Based on the decomposition algorithm, Shift-Addition Units (SAUs)-based circuits are designed to conduct matrix multiplication and can be reused during the processing of three types. As a result, this unified architecture is capable of performing all types and sizes in VVC. The synthesis results indicate that this architecture achieves an area reduction of 37.9% ~ 72.2% compared with related works for 32-point transforms.