You can't tell the dimensions from the area. There are an infinite number of different shapes that all have the same area. Even if you only consider rectangles, there are still an infinite number of rectangles with different dimensions that all have the same area.
Here are a few. All of these have areas of 256:
1 x 256
2 x 128
3 x 85 and 1/3
4 x 64
5 x 51.2
6 x 42 and 2/3
7 x 36 and 4/7
8 x 32
9 x 28 and 4/9
10 x 25.6
11 x 23 and 3/11
12 x 21 and 1/3
If you want a square, then it's [ 16 x 16 ].
If you want a circle, then the diameter is 18.054(rounded).
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A square with a side length of 16 inches has an area of 256 square inches.
New area = 256 so new side = sqrt 256 = 16 so old side = 12 (so old area = 144)
A square TV screen with a side length of 16 inches has an area of 256 square inches.
256 sqcm
If the square has an area of 256 square feet then each side of the square is 16 feet because the square root of 256 is 16