What is the area of the square below?

Diagonal of square would have length 24. You can treat diagonal as leg of isosceles triangle.

Recall that 45-45-90 isosceles triangle has side ratio 1:1:√2 and so ratio of triangle sides would be 12√2 : 12√2 : 24 (you just multiple ratio by 12√2)

So then sides would be 12√2

Area would be (12√2)² = 288

So answer is 288 cm²