Final answer:
To find the area of the square with side length (3 + √2), square the expression to get 11 + 6√2. Therefore, the area of the square is represented by option D: 11 + 6√2.
Step-by-step explanation:
One way to find a square's area is to square one of its sides' lengths. Given the side length of the square is 3 + √2, to find the area, we square this expression:
(3 + √2)² = (3² + 2·(3)·(√2) + (√2)²)
- 3² = 9
- 2·(3)·(√2) = 6√2
- (√2)² = 2
Add these values together to get the area: 9 + 6√2 + 2, which simplifies to 11 + 6√2.
Therefore, the correct answer is D: 11 + 6√2.