In geometry, a **rectangle** is a defined as a quadrilateral polygon in which all four angles are right angles.

From this definition, it follows that a rectangle has two pairs of opposite sides of equal length; that is, a rectangle is a parallelogram. A square is a special kind of rectangle where all four sides have equal length; that is, a square is both a rectangle and a rhombus. A rectangle that is not a square is colloquially known as an *oblong*.

Of the two opposite pairs of sides in a rectangle, the length of the longer side is called the *length* of the rectangle, and the length of the shorter side is called the *width*. The area of a rectangle is the product of its length and its width; in symbols, *A* = *l**w*. For example, the area of a rectangle with a length of 5 and a width of 4 would be 20, because 5 × 4 = 20. See the picture above right.

In calculus, the Riemann integral can be thought of as a limit of sums of the areas of arbitrarily thin rectangles.

## Oblong

The word **oblong** was once commonly used as an alternate name for a rectangle. In his translation of Euclid's *Elements*, Sir Thomas Heath translates the Greek word ετερομηκες [*hetero mekes* – literally, "different lengths"] in Book One, Definition 22 as oblong. "Of Quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right angled but not equilateral...".

## See also

## References

Heath, Sir Thomas L. *The Thirteen Books of Euclid's Elements*. 2nd ed. 3 vols. 1926; rpt. New York: Dover Publications, Inc., 1956.