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.
![convex quadrilateral, concave quadrilateral, and complex quadrilateral](/sites/default/files/users/Mathalino/plane-geometry/010-convex-concave-complex-quad.jpg)
The following formulas are applicable only to convex quadrilaterals.
General Quadrilateral
![General Quadrilateral](/sites/default/files/images/general-quadrilateral.jpg)
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 d1 and d2
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