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For many people, the rhombus—originally called a "rhomb" (see In Brief, "The origin of the rhombus"; the associated adjective is still "rhombic")—is characterized by its acute angles pointing upward and downward. Yet, as Euclid already observed, this quadrilateral is defined by the equal lengths of its sides. Its ability to form tilings accounts for its use in architecture and decoration.
For the familiar convex quadrilaterals, the classification criteria are, first, whether the sides are parallel, then whether their lengths are equal, and finally whether there are any right angles.
A square is a special kind of rhombus. Anyone can easily calculate the area of a square, but what about the area of a rhombus? Similarly, a square has both a circumcircle and an incircle. What happens in the case of a rhombus?
