Quadrilateral

Polygon with four sides and four vertices.

The sum of the internal angles of a quadrilateral is 360°.

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° and its opposite sides are parallel and of equal length.

The area of a rectangle is given by the formula:

$\text{Area}=l \times w$

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

Square

The internal angles of a square are all equal to 90° 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:

$\text{Area}=s^2$

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:

$\text{Area}=d_1 \times d_2$

where d₁ and d₂ 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:

$\text{Area}=b \times h$

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:

$\text{Area}=\frac{a+b}{2} \times h$

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:

$\text{Area}=\frac{p \times q}{2}$