1. **State the problem:** We need to find the total area of the rectangular faces of the 3D shape. The given dimensions are 7 cm and 8 cm for the edges of one rectangular face. 2. **Identify the rectangular faces:** Since the shape is 3D and one rectangular face has edges 7 cm and 8 cm, the adjacent rectangular faces will share these edges with the third dimension (height or depth) unknown. However, based on the problem, we only have these two edges, so we assume the shape is a rectangular prism with edges 7 cm, 8 cm, and a third edge (let's call it $h$). 3. **Formula for area of rectangular faces:** A rectangular prism has 3 pairs of rectangular faces. The total surface area is: $$\text{Total Area} = 2(lw + lh + wh)$$ where $l$, $w$, and $h$ are the lengths of the edges. 4. **Given data:** We have $l = 7$ cm, $w = 8$ cm, but $h$ is not given. Since the problem only mentions these two edges and the purple face formed by them, we can only find the area of that single rectangular face: $$\text{Area} = l \times w = 7 \times 8 = 56$$ 5. **Conclusion:** Without the third dimension, the total area of all rectangular faces cannot be determined. The area of the purple rectangular face is $56$ cm$^2$. **Final answer:** The area of the purple rectangular face is $56$ cm$^2$.