Solution:
Note that:
- Area of square = s² (s = Side length)
Finding the leg of a square with area of 369 units²
- c² = 369
- => c = √369 units
Finding the leg of a square with area of 81 units²
- b² = 81
- => b = √81 = 9 units
Finding side length a using Pythagoras theorem
- (√369)² = 9² + a²
- => 369 = 81 + a²
- => 369 - 81 = a²
- => 288 = a²
- => a = √288 = √144 x 2 = √12 x 12 x 2 = 12√2 units
Finding the missing area of the square.
- Area of square = a²
- => Area of square = a² = (a)²
- => Area of square = (12√2)²
- => Area of square = (12√2)(12√2) = 288 units²
Option D is correct.