The area of the baseball diamond is 8192 sq. units.
We assume the square-shaped, baseball diamond to be ABCD with A = (0, 64), B = (64, 0), C = (0, -64), and D = (-64, 0).
The side of the square can be computed using the distance formula,
D = √((x₂ - x₁)² + (y₂ - y₁)²), when the endpoints of a line are (x₁, y₁) and (x₂, y₂).
Thus, the side of the square,
a = √((x₂ - x₁)² + (y₂ - y₁)²),
or, a = √((64 - 0)² + (0 - 64)²) {Considering A(0,64) and B(64, 0) as the endpoints,
or, a = √(64² + (-64)²),
or, a = √(4096 + 4096),
or, a = 64√2 units.
Now, the area of the square can be calculated using the formula, A = a², where A is the area and a is the side of the square.
Thus, the area of the square = (64√2)² = 4096*2 = 8192 sq. units.
Thus, the area of the baseball diamond is 8192 sq. units.
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