Rectangle

A rectangle is a quadrilateral in a plane with four angles, each of which is a right angle (90 degrees). Because of the equal angles, opposite sides are parallel and equal in length. Therefore, a rectangle is a type of parallelogram.

A rectangle is defined by two measurements: length and width. When these two measurements are equal, the shape becomes a square. This means that a square is a special type of rectangle, but not every rectangle is a square.

Basic Properties

The sum of the interior angles of a rectangle is 360 degrees, which is true for any quadrilateral. The two diagonals are equal in length and bisect each other at the center, so each diagonal divides the other into two equal parts.

A rectangle has two lines of symmetry when it is not a square: one along its length at the center and one along its width. It also has rotational symmetry of 180 degrees. A square, by contrast, has four lines of symmetry.

Calculating Area and Perimeter

The area of a rectangle is found by multiplying length by width: A = d × b. The perimeter is twice the sum of length and width: P = 2(d + b). The length of the diagonals is calculated using the Pythagorean theorem: the square root of (d² + b²).

Applications

The rectangle is one of the most common shapes seen in architecture, art, and design. Standard paper, doors, computer screens, mobile phones, and the flags of many countries have a rectangular form. In mathematics, the rectangle is fundamental to the coordinate system and to dividing the areas of other complex shapes.