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THE FEUTEX TOOLKIT

Cyclic Quadrilateral from Four Sides

Calculate area and diagonal lengths of a convex cyclic quadrilateral.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
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FormulaArea = sqrt(((-a+b+c+d)/2)*((a-b+c+d)/2)*((a+b-c+d)/2)*((a+b+c-d)/2)); Diagonal Ac = sqrt((a*c+b*d)*(a*d+b*c)/(a*b+c*d)); Diagonal Bd = sqrt((a*c+b*d)*(a*b+c*d)/(a*d+b*c))
Sources and model references

Made for real tasks

  • Calculate area and diagonal lengths of a convex cyclic quadrilateral.
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Worked example

Inputs

Side AB
3 length
Side BC
4 length
Side CD
5 length
Side DA
6 length

Expected results

Area
18.97366596 length²
Diagonal Ac
5.940177968 length
Diagonal Bd
6.565459859 length

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter side ab, side bc, side cd, side da.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "a": 3,
  "b": 4,
  "c": 5,
  "d": 6
}

Accuracy and scope

Assumes four vertices lie on one circle in the supplied side order; not valid for a general quadrilateral.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.