Polygon with four sides and four vertices.

The sum of the internal angles of a quadrilateral is $360\degree$.

There are six special quadrilaterals: rectangle, square, rhombus, parallelogram, trapezoid/trapezium and kite.

Rectangle

The internal angles of a rectangle are all equal to $90\degree$ and its opposite sides are parallel and of equal length. 

The area of a rectangle is given by the formula:

where $l$ is the length and $w$ the width of the rectangle.

Square

The internal angles of a square are all equal to $90\degree$ and its opposite sides are parallel and all of its sides have equal length. It is the only regular quadrilateral.

The area of a square is given by the formula:

where $s$ is the length of the side of the square.

Rhombus

The opposite internal angles of a rhombus are equal, its opposite sides are parallel and all of its sides have equal length. 

The area of a rhombus is given by the formula:

where $d_1$ and $d_2$ are the lengths of the two diagonals of the rhombus.

Parallelogram

The opposite internal angles of a parallelogram are equal, its opposite sides are parallel and equal in length.

The area of a parallelogram is given by the formula:

where $b$ is the base and $h$ is the height of the parallelogram, i.e., it is the perpendicular distance between the base and the parallel side.

Trapezoid/trapezium

A trapezoid/trapezium has a pair of opposite sides parallel. These sides are called bases.

The area of a trapezoid/trapezium is given by the formula:

where $a$ and $b$ are the bases and $h$ the height of the trapezoid/trapezium, like the height of the parallelogram.

Kite

A kite has two pairs of sides where each pair have the same length share the same vertex; we call these sides are adjacents. Also, the angles formed where the two pairs meet are equal.

The area of a kite is given by the formula:

where $p$ and $q$ are the diagonals of the kite.