An instrument that measures area is called a planimeter. A planimeter is a mechanical device used to calculate the area of a two-dimensional shape by tracing its outline. It works by integrating the distance traced by a point on the planimeter's arm as it moves around the shape, providing an accurate measurement of the enclosed area.
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planimeter
http://en.wikipedia.org/wiki/Planimeter
A sextant.
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The area of square is : 36.0
Miles measures distance. Square miles measures area. Therefore, you can not compare the two. It is like comparing feet and cups.
There is not an instrument designed to measure the volume of a rectangular box. You would use a ruler or tape measure or similar to measure its linear dimensions and a brain to multiply them together.