Area of an arbitrary quadrangle, formulas and calculator for calculating online.
To calculate the area of an arbitrary quadrilateral, various formulas are used, depending on the known source data. Below are formulas and a calculator that will help you calculate the area of an arbitrary quadrangle or check already performed calculations.
At the end of the article there are links for calculating particular cases of quadrangles: square, trapezoid, parallelogram, rectangle, rhombus.
Table with quadrangle area formulas (at the end of the page)
1
The area of the quadrangle along the diagonals and the angle between them
2
The area of the quadrangle through the sides and the angles between these sides
When calculating the area of a quadrangle using this formula, you must first calculate the perimeter of the quadrangle by the formula:
3
The area of a quadrilateral inscribed in a circle, calculated according to the Brahmagupta Formula
This formula is valid only for quadrangles around which a circle can be described.
When calculating the area of a quadrangle using this formula, you must first calculate the perimeter of the quadrangle by the formula:
4
The area of the quadrangle into which you can enter a circle
This formula is valid only for quadrangles into which you can enter a circle. The inscribed circle must have points of contact with all four sides of the quadrangle.
When calculating the area of a quadrangle using this formula, you must first calculate the perimeter of the quadrangle by the formula:
5
The area of the quadrangle into which the circle defined by the sides and the angles between them can be entered
This formula is valid only for quadrangles into which you can enter a circle. The inscribed circle must have points of contact with all four sides of the quadrangle.
Note:
If the angle is specified in radians in the source data, then for conversion to degrees you can use the formula: 1 ×
Table with quadrangle area formulas
initial data (active link to go to the calculator) 
sketch  formula  
1  diagonal and angle between them  
2  sides and angles between these sides 
where ,


3  parties 
where


4  sides and radius of the inscribed circle 
where


5  sides and angles between them 
Area of special cases of quadrangles
To calculate special cases of quadrangles, you can use the formulas and calculators given in other articles of the site: