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 ${\displaystyle \Box ABCD}$.

Rectangles hold the following properties:

• Opposite sides are of equal length (congruent)
• Adjacent sides meet at right angles
  • All four angles are of equal measure (congruent)
  • All four angles are right angles
    • Adjacent angles are supplementary
  • Opposite sides are parallel
    • Parallelogram
• Diagonals are of equal measure (congruent)
  • Diagonals bisect one another

Area

The area of a rectangle is computed as the product of its length and its width:

${\displaystyle A = lw}$

Perimeter

The perimeter of a rectangle is computed as:

${\displaystyle P = 2(l + w)}$

Circumcircle

The circumradius of a rectangle is:

${\displaystyle R= \frac{\sqrt{l^2+w^2}}{2}}$

Incircle

The inradius of a rectangle is:

${\displaystyle r= \frac{lw}{l+w}}$

Diangle length

The diangle length of a rectangle is: