Calculating the area of any quadrilateral

Any Quadrilateral

Every quadrilateral is a polygon with four sides of any length connected together at the corners. The method of calculation for quadrilaterals is triangulation, which requires you to know the lengths of one of the two diagonals.

Through this formula, it's possible to find out the area of any quadrilateral, no matter if it's a parallelogram, rhombus, trapezoid – in short, every 4-sided surface expect a crossed quadrilateral.

Calculation of the quadrilateral

Triangulation calculation method

quadrilateral

* Be careful to respect the order of the sides and use the diagonal 'ab' as shown on the drawing, otherwise you may get a wrong result.

Side length:
side a
 
side b
 
diagonal ab
 
side c
 
side d
 
Units: 
Decimal places: 
Units angles: 
Surface: 
0,87 cm2
Perimeter: 
4,00 cm
Quadrilateral angles
(alpha) α
60,00 °
(beta) β
120,00 °
(gamma) γ
60,00 °
(delta) δ
120,00 °

The Angles of a Quadrilateral

Starting now, this page will show the value of the 4 angles. You can choose between degrees, radians or gradians.

The calculation is done as follows: find the sum of the squares of the two adjacent sides of the angle, which is then subtracted from the square of the opposite diagonal. Then, divide the result of this "addition/subtraction" by the product of the two adjacent sides times two. Finally, you calculate the arccosine of the above result. What a cinch!  Now for those who need it, you can find aspirin, Tylenol or other headache medicine at your nearest drug store…

Quadrilaterals at Home

Knowing the calculation of any quadrilateral is useful for determining the area of household objects with precision – even more so in older homes. It's common to have rooms in which the walls are not perpendicular with each other, making them not just rectangles, but various types of quadrilaterals.

All the same, calculating the land surface area is very difficult if the surface is considered a rectangle, which is hardly ever the case. By knowing its four sides, one of its two diagonals and using the formula on this page, your results will be spot-on.

Google Earth and Quadrilaterals

By using the scale tool on Google Earth and filling in this formula, it's easy to find (very closely at least) the area of geographical locations which interest you.

Crossed Quadrilaterals

A quadrilateral may be convex (the usual case), concave (forming a recess) or crossed. In this last case, it creates two triangles. To calculate its features, the simplest way is to calculate the features of the two triangles which make up the crossed quadrilateral.