Calculator Inputs
The page stays in one vertical flow. The input grid becomes three columns on large screens, two on medium screens, and one on mobile.
Formula Used
1) Coordinate method
Area uses the shoelace rule:
Area = 1/2 × |Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|
Perimeter is the sum of the four side distances. Each side uses the distance formula between consecutive vertices.
2) Side and opposite angle method
Bretschneider’s formula handles a general convex quadrilateral:
Area = √[(s−a)(s−b)(s−c)(s−d) − abcd cos²((A+C)/2)]
s = (a+b+c+d)/2. When the shape is cyclic, A + C = 180°, so the cosine term becomes zero.
3) Diagonal and included angle method
When both diagonals and their included angle are known:
Area = 1/2 × p × q × sin(θ)
How to Use This Calculator
- Pick the solving mode that matches your available measurements.
- Enter a unit label such as cm, m, or ft.
- Set the decimal precision for display formatting.
- Enter values carefully. Coordinate points should follow the polygon boundary.
- Press Calculate Polygon to show results above the form.
- Review the metrics table and Plotly graph for geometry insight.
- Use the CSV or PDF buttons to save the result summary.
Example Data Table
| Example | Inputs | Expected Output |
|---|---|---|
| Coordinates | A(0,0), B(4,0), C(4,3), D(0,3) | Rectangle, area 12, perimeter 14, diagonals 5 |
| Sides + opposite angle sum | a=5, b=6, c=5, d=6, A+C=180° | Cyclic quadrilateral, area 30, perimeter 22 |
| Diagonals + angle | p=10, q=8, θ=60° | Area ≈ 34.6410 |
FAQs
1) What is a four sided polygon?
A four sided polygon is a quadrilateral. It has four vertices, four edges, and interior angles that sum to 360 degrees.
2) Which method should I choose?
Use coordinates when vertex locations are known. Use sides plus opposite angle sum for measured edges. Use diagonals plus angle when diagonal surveying data is available.
3) Why do coordinate points need boundary order?
The shoelace rule assumes the polygon path follows its outline. Random point order can create self crossing shapes and wrong area values.
4) What does cyclic quadrilateral mean?
A cyclic quadrilateral has all four vertices on one circle. Its opposite angles add to 180 degrees, which simplifies the area formula.
5) Can this calculator find every missing dimension?
No. Some quadrilateral properties need more measurements. The calculator solves reliably only from the information set supported by the chosen method.
6) Does the graph always show the exact shape?
The plotted shape is exact for coordinate input. Other methods show a comparison chart because unique vertex coordinates are not determined from the provided data alone.
7) Why do I see mixed quantities in bar charts?
The bar chart is a quick visual summary. Lengths, angles, and area use different units, so compare trend sizes only, not physical equivalence.
8) Are the exports based on the visible results?
Yes. The CSV and PDF tools save the current summary table shown after calculation, making it easy to document one result set at a time.