1. Problem statement: Find the surface area of a cube with side length $a$. 2. Formula and rules: A cube has 6 congruent square faces. Each square face has area $a^2$. Therefore the surface area is the sum of 6 face areas. 3. Formula (display): $$S = 6a^2$$ 4. Explanation: We add six copies of $a^2$ because there are 6 faces. 5. Intermediate work: Write the total area as a sum of face areas: $S = a^2 + a^2 + a^2 + a^2 + a^2 + a^2$. Then combine like terms to get the simplified form. Display of simplification: $$S = 6a^2$$ 6. Example (numeric): If $a=3$, then compute step by step. First compute the square: $3^2 = 9$. Then multiply by 6: $S = 6\times 9$. Evaluate: $S = 54$. 7. Final answer: The surface area of a cube of side length $a$ is $S = 6a^2$.