A quadrilateral is a four sided polygon. The sum of interior angles for all quadrilaterals must be equal to 360 degrees. There are five main types of quadrilaterals each having its own features.

These two rules apply to all quadrilaterals:

  1. The perimeter measure of any four-sided figure is always the sum of its side lengths.
  2. The sum of the angle measures of a quadrilateral is always 360 degrees.

1. Square

A square is a rectangle with four equal sides, which means you can easily find its area when you know the length of only one side.

square

  • All sides are equal in length.
  • All angles are right angles.
  • Opposite sides are parallel.
  • Perimeter = 4 × (side) = 4 × L
  • Area = (Side) × (Side) = L × L = L2

2. Rectangle

A rectangle is a parallelogram with four right angles.

rectangle

  • Opposite sides are equal in length.
  • Opposite sides are parallel.
  • All angles are right angles.
  • Perimeter = 2 × (Length + Breadth) = 2 × (L + B)
  • Area = (Length) × (Breadth) = L × B

3. Parallelogram

parallelogram

  • Opposite sides are equal in length and parallel.
  • Opposite angles are equal.
  • Adjacent angles are supplementary. The measures of the adjacent angles add up to 180 degrees.
  • The diagonals bisect each other. In other words, they cross at the midpoint of both diagonals.

Perimeter = 2 × (Length + Breadth) = 2 × (L + B)

Area: The area of any parallelogram is its base times its height. You can use the Pythagorean theorem to help you find the height of a parallelogram. When you drop a perpendicular line from one corner to the base to create the height, the line becomes the leg of a right triangle.

Area = (Length) × (Height) = L × h

4. Rhombus

A rhombus has four equal sides but not necessarily four right angles.

rhombus

  • All sides are equal in length (all angles are not equal).
  • Adjacent angles are supplementary.
  • Opposite angles are equal.
  • Diagonals bisect each other at right angles. 
  • Perimeter = 4 × (Side) = 4 × L
  • Area = (multiple of diagonals)/2 = ½d1d2

5. Trapezoid

A trapezoid is a quadrilateral with just one set of parallel sides. The parallel sides are called the bases, and the other two sides are called the legs. In an isosceles trapezoid, the legs of the quadrilateral are the same length.

You can find the area of a trapezoid as long as you know the length of both bases and the height.

trapezoid

  • Only one pair of sides is parallel.
  • Perimeter = Sum of sides = A + B + C + D
  • Area = (Height) × (Sum of parallel sides)/2 = (h) × (A + B)/2 = ½(b1 + b2)h