The information given in the question does not give the shape of the area so it is impossible to answer the question.
The most compact shape would be circular with a radius of just over 8.92 feet.
With each of infinitely many polygonal shapes, there are infinitely many possible dimensions. Consider a rectangle.
Let its length be L feet where L is any value > sqrt(250).
Let is breadth be B = 250/L feet.
Then area = L*B = L*250/L = 250 sq feet.
But L can have infinitely many values and therefore the dimensions of the rectangle are indeterminate.
For example, L = 25, B = 10
L = 250, B = 1
L = 25000, B = 0.01
and so on.
And then there are non-rectangular quadrilaterals, triangles, pentagons, hexagons, ... .
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The dimensions will be square feet.
The dimensions of square feet is Length2 or L2
Square feet have dimensions L2 while cubic feet have dimensions L3 so they are not interchangeable.
The dimensions would be 40 feet by 40 feet.
about 5000 square feet, if the corners are roughly square.