Geometry

Quadrangle area

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

The area of the quadrangle along the diagonals and the angle between them
... preparation ...
d1 - diagonal
d2 - diagonal
α° - Angle between diagonals


2

The area of the quadrangle through the sides and the angles between these sides

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:

... preparation ...

a - side
b - side
c - side
d - side
α° - angle between parties
β° - angle between parties


3

The area of a quadrilateral inscribed in a circle, calculated according to the Brahmagupta Formula

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:

... preparation ...

a - side
b - side
c - side
d - side


4

The area of the quadrangle into which you can enter a circle

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:

... preparation ...
a - side
b - side
c - side
d - side
r - radius of inscribed circle


5

The area of the quadrangle into which the circle defined by the sides and the angles between them can be entered

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.

... preparation ...

a - side
b - side
c - side
d - side
α° - angle between parties
β° - angle between parties

Note:

If the angle is specified in radians in the source data, then for conversion to degrees you can use the formula: 1 × (180/π)° = 57,296°



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:



Share this link: