Rectangle

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A 5 by 4 rectangle

In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. A rectangle with vertices ABCD would be denoted as ABCD.

From this definition, it follows that a rectangle has two pairs of parallel sides; 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.

Normally, 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 $5 \times 4 = 20$ .

In a rectangle the diagonals cross each other at their respective midpoints, under the same argument as for parallelograms. Unlike general parallelograms the two diagonals of a rectangle have the same length, the length of the diagonal can be found using the Pythagorean theorem.

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