Common quadrilaterals
Last updated: 15 Nov 2008
The most common quadrilaterals that you will see in the GMAT are the parallelogram, the rhombus, the rectangle and the square.
Parallelogram
A parallelogram is the quadrilateral formed by 2 pairs of parallel sides (thus the name).
Properties
- 2 pairs of parallel sides.
- 2 pairs of equal sides.
- Diagonals bisect each other i.e. cut each other exactly in half.
- Opposite angles are equal.
Rhombus
A rhombus is a parallelogram in which all the sides are equal.
Properties
- 2 pairs of parallel sides.
- 4 equal sides.
- Diagonals bisect each other i.e. cut each other exactly in half.
- Diagonals are perpendicular.
- Opposite angles are equal.
Rectangle
A rectangle is a parallelogram where all the angles are right angles (90°).
Properties
- 2 pairs of parallel sides.
- 2 pairs of equal sides.
- Diagonals bisect each other i.e. cut each other exactly in half.
- Diagonals are equal.
- All angles are 90°.
Square
A square is a special kind of parallelogram (and rhombus and rectangle) where all the sides are equal and all the angles are right angles.
Properties
- 2 pairs of parallel sides.
- 4 equal sides.
- Diagonals bisect each other i.e. cut each other exactly in half.
- Diagonals are perpendicular.
- Diagonals are equal.
- All angles are equal.
Area
The area of all the previous quadrilaterals, i.e the parallelogram, rhombus, rectangle and square is calculated in exactly the same way; Area = base x height.
Note: In all cases height is measured perpendicularly from the base so in the cases of a rhombus and a parallelogram it is not the same as the length of the side. See diagram below.
