1. **Problem statement:** Calculate the surface area of a triangular prism with base side length $a=6$ cm, height of the triangle $h_a=5.2$ cm, and prism height $h_k=19.8$ cm. 2. **Formula for surface area of a triangular prism:** The surface area $O$ consists of the two triangular bases plus the three rectangular lateral faces: $$O = 2 \cdot G + U \cdot h_k$$ where $G$ is the area of the triangular base and $U$ is the perimeter of the base. 3. **Calculate the base area $G$:** The base is an equilateral triangle with side $a=6$ cm, so $$G = \frac{a \cdot h_a}{2} = \frac{6 \cdot 5.2}{2} = 15.6 \text{ cm}^2$$ 4. **Calculate the perimeter $U$ of the base:** Since the base is equilateral, $$U = 3 \cdot a = 3 \cdot 6 = 18 \text{ cm}$$ 5. **Calculate the surface area $O$:** $$O = 2 \cdot 15.6 + 18 \cdot 19.8$$ $$O = 31.2 + 356.4 = 387.6 \text{ cm}^2$$ 6. **Answer:** The surface area of the prism is $$\boxed{387.6 \text{ cm}^2}$$