C

Step 1: ΔABC is a right triangle.[Height AB is perpendicular to BC and the lateral edge AC is the hypotenuse.]

Step 2: BC² + AB² = AC²[Apply Pythagorean theorem.]

Step 3: BC² + 4² = 5²[Substitute height, AB = 4 and lateral edge, AC = 5.]

Step 4: BC² + 16 = 25[Simplify.]

Step 5: BC² = 9[Subtract 16 from both sides.]

Step 6: BC = 9 = 3 cm.[Take square root on both sides.]

Step 7: Diagonal of the square base = 2 × BC[BC is half the diagonal of the square base.]

Step 8: = 2 × 3 = 6 cm.[Substitute and multiply.]

Step 9: Area of a square = 12 × product of the diagonals[Formula for the area of a square in terms of the measure of diagonals.]

Step 10: = 12 × 6 × 6 = 18[The diagonals of a square have equal measures. Substitute the values.]

Step 11: The base area of the square pyramid is 18 cm.².