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area of rhombus = half of product of its diagonals.

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That is true but incomplete answer. If you know the lengths of the sides, r, and a angle which measures x, then area = r^2*sin(x).

Incidentally, it does not matter whether you know the value of an acute angle or an obtuse angles: they are supplementary and so their sines are the same.

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Q: Area of a rhombus
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