Rectangle

In geometry, a rectangle is a closed planar quadrilateral with four right angles. It follows that opposite sides are of equal lengths; that is, a rectangle is a parallelogram. If adjacent sides have lengths a and b, the area of the rectangle is a square

$A=ab.$

If a = b the rectangle is a square.

Unlike a parallelogram or a rhombus, the diagonals of a rectangle are congruent to each other. It is also a special case of a trapezoid (in North America) or trapezium (in Britain and elsewhere). A rectangle with vertices ABCD would be denoted as  ABCD. The dual polygon of a rectangle is a rhombus. The three-dimensional counterpart of a rectangle is a cuboid, also called a rectangular parallelepiped.

Students in the US are sometimes taught this formula:

• Rectangle (four congruent angles) + Rhombus (four congruent sides) = Square (four congruent angles and four congruent sides)

A 5 by 4 rectangle

Every rectangle tilable by a finite number of squares or isosceles right triangles has commensurable sides. The 5 x 4 rectangle illustrated is an example of this. The golden rectangle is an example of a rectangle whose sides are incommensurable; that is, their ratio is an irrational number.

A rectangle partitioned into a finite number of similar tiles is called a perfect rectangle if no two tiles are the same size. Otherwise it is an imperfect rectangle. The tiles may be squares, rectangles, or right triangles.

External links

• Weisstein, Eric W. "Rectangle". MathWorld.
• Definition and properties of a rectangle With interactive animation
• Area of a rectangle with interactive animation