Definitions

# Rectangle

[rek-tang-guhl]

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 .

From this definition, it follows that a rectangle has two pairs of parallel sides; that is, a rectangle is a parallelogram. An equilateral rectangle is known as a square.

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, $A=lw$. 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.

A rectangle may be constructed from a series of squares. If it can be constructed from squares of all different sizes, it is a 'perfect rectangle'. If this is not possible, it is an imperfect rectangle.