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Let's call the diagonal distance across the plaza D. Since the plaza is square, we can use the Pythagorean theorem to find D:
D^2 = 5050^2 + 5050^2
D^2 = 2 * (5050^2)
D = sqrt(2 * (5050^2))
Now we can simplify the expression:
D = 5050 * sqrt(2)
So, the diagonal distance across the plaza is 5050√2 meters.