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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 \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
  • 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:

A = lw

Perimeter

The perimeter of a rectangle is computed as:

P = 2(l + w)

Circumcircle

The circumradius of a rectangle is:

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

Incircle

The inradius of a rectangle is:

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

Diangle length

The diangle length of a rectangle is:

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