# The Quadrilateral

Quadrilateral is a polygon of four sides and four vertices. It is also called tetragon and quadrangle. In the triangle, the sum of the interior angles is 180°; for quadrilaterals the sum of the interior angles is always equal to 360°

**Classifications of Quadrilaterals**

There are two broad classifications of quadrilaterals; *simple* and *complex*. The sides of simple quadrilaterals do not cross each other while two sides of complex quadrilaterals cross each other.

Simple quadrilaterals are further classified into two: *convex* and *concave*. Convex if none of the sides pass through the quadrilateral when prolonged while concave if the prolongation of any one side will pass inside the quadrilateral.

The following formulas are applicable only to convex quadrilaterals.

**General Quadrilateral**

Any convex quadrilateral can use the following formulas:

Perimeter, P (applicable to all quadrilaterals, simple and complex)

Area, A

where

s = semi perimeter = ½P

$\varphi$ = ½ (A + C) or $\varphi$ = ½ (B + D)

The area can also be expressed in terms of diagonals d_{1} and d_{2}