Formulae for calculating the area of a quadrilateral non-cyclic

In summary, there are two different formulas for calculating the area of a non-cyclic quadrilateral. The first formula requires 6 values, including the four edges and two diagonals. The second formula only needs 4 values, but it may not work for all types of quadrilaterals. There are also other formulas for calculating the area of a quadrilateral, such as Bretschneider's formula, which may require even more values.
  • #1
Bruno Tolentino
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I want knows if a formula for calculate the area of a quadrilateral non-cyclic needs of just four values (the values of the four edges) or if is necesseray 6 values (the values of the four edges MORE os values of the two diagonals)?

This formula needs of 6 values (a,b,c,d,p,q):
1a04d408f073f30a1edd47b9f4501566.png


OBS: s = (a+b+c+d)/2

And this formula needs of just 4 (a,b,c,d):
3227d258f1f0437e6cad6f6000c9c479.png


But, I tested this second formula in the geogebra and it don't works...

Sources:
http://en.wikipedia.org/wiki/Trapezoid#Area
http://en.wikipedia.org/wiki/Quadrilateral#Non-trigonometric_formulas
https://en.wikipedia.org/wiki/Bretschneider's_formula#Related_formulas
 
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  • #2
The four edges are obviously not sufficient. Start with a square (side length=1) - area =1. Now take a pair of diagonally opposite corners and move them toward each other, while keeping the side lengths constant. When they meet, the resultant quadrilateral area = 0.
 
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  • #3
And 4 sides and 1 diagonal is not sufficient either. Consider a shape with sides 1, 1, 0.8, 0.8 in that order. Now the 0.8 v can be inside, or outside (convex or concave) with the area different.
 
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FAQ: Formulae for calculating the area of a quadrilateral non-cyclic

1. What is the formula for finding the area of a quadrilateral non-cyclic?

The formula for calculating the area of a quadrilateral non-cyclic is: Area = (1/2) x (sum of opposite sides) x (distance between opposite sides).

2. How do you determine the distance between opposite sides in a quadrilateral non-cyclic?

To find the distance between opposite sides in a quadrilateral non-cyclic, you can use the Pythagorean theorem to calculate the length of the diagonal. Then, you can use this diagonal as the distance between opposite sides in the formula for area.

3. Can the formula for calculating the area of a quadrilateral non-cyclic be used for all types of quadrilaterals?

Yes, the formula can be used for all types of quadrilaterals as long as the sides are not cyclic, meaning they do not lie on a circle.

4. Is there a specific unit of measurement that should be used when using the formula for calculating the area of a quadrilateral non-cyclic?

No, the formula can be used with any unit of measurement as long as all the measurements (opposite sides and distance) are in the same unit.

5. How accurate is the formula for calculating the area of a quadrilateral non-cyclic?

The formula is accurate as long as the measurements used are precise and the quadrilateral is not a concave shape. If the measurements are rounded or the shape is concave, the calculated area may be slightly off.

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