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It depends first of all on whether or not the decagon is regular. If it is not regular, there are two main options: one is to divide it into sections for which there are simple formulae, and sum the results. The alternative is to copy the shape onto a lamina of uniform mass, measure the mass (or weight) of the shape and of a square of unit size and use the ratio of the masses to estimate the area of the shape.

Area of shape = (Mass of copied shape/Mass of unit square)*Area of unit square

The last term has value 1, but is included so that the equation is balanced in its dimensions.

If the shape is regular, then it depends on what information is given.

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Q: How do you measure the square footage of a decagon?
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