To overcome the limitations imposed by externally active excitation conditions and to expand the feasibility and effectiveness of tuning the microwave absorption performance of metamaterials, this paper presents an innovative research work. Specifically, a flexible metamaterial absorber based on the geometric principle of equal-area transformation of triangles (i.e., triangles with equal base and height possess equal area) is designed and proposed. The proposed absorber features a unique physical structure and good flexibility. When a horizontal stretching strain is applied to the flexible dielectric substrate, the triangular copper film on it undergoes out-of-plane buckling or rigid-body tilting due to the Poisson effect and modulus mismatch, thereby altering the shape of the copper film unit and consequently tuning the resonant frequencies of the metamaterial absorber. Combined with finite element simulations, when the metal pattern is varied by stretching the flexible dielectric layer, as the stretching length increases and the pattern transforms from a right triangle to an isosceles triangle, the absorption peak shifts toward higher frequencies, and the absorption intensity gradually increases. When the pattern deforms into an isosceles triangle, the proposed absorber achieves a peak absorption rate of 99% at 5.636 GHz, which is in good agreement with experimental results. To deeply explore the physical mechanism underlying the tunable absorption peak frequency of the microwave metamaterial based on equal-area transformation, two targeted circuit models are constructed. The first one is a resonant circuit model, established based on the characteristics of the electromagnetic field distribution. For the microwave metamaterials, the electromagnetic field distribution plays a decisive role in determining the absorption performance. Different electromagnetic field distribution patterns lead to variations in the interaction between the metamaterial and incident microwaves, thereby affecting the absorption frequency. The second one is an equivalent circuit model, established mainly based on the structural dimensions. The structural dimensions of the microwave metamaterial are key factors influencing its electromagnetic response. Different structural dimensions induce distinct electromagnetic resonance modes within the metamaterial, thereby altering the absorption frequency. The absorption frequencies calculated by both circuit models are in good agreement with those obtained from full-wave electromagnetic simulations. This indicates that the reconstruction of electromagnetic field distribution and the polarization charge accumulation effect induced by equal-area transformation are the core mechanisms governing the tunable absorption performance. The results presented in this paper can provide guidance and reference for the structural design and tunability mechanism research of microwave absorbing metamaterials.