# Rectangle

Missing image
Rectangle4x5.png
A 5 by 4 rectangle

In geometry, a rectangle is 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 = lw. 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...".

## References

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

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