Enter Ordered Vertex Coordinates
Enter the five vertices in the order you would trace the pentagon boundary.
Example Data Table
| Vertex | X | Y |
|---|---|---|
| V1 | 0 | 0 |
| V2 | 5 | 0 |
| V3 | 6 | 3 |
| V4 | 3 | 6 |
| V5 | -1 | 4 |
| Sample Output | Value |
|---|---|
| Area | 30.0000 square units |
| Perimeter | 21.0002 units |
| Centroid | (2.4667, 2.6000) |
| Orientation | Counterclockwise |
Formula Used
The calculator uses the shoelace formula on five ordered vertices:
Area = 1/2 × |(x1y2 + x2y3 + x3y4 + x4y5 + x5y1) − (y1x2 + y2x3 + y3x4 + y4x5 + y5x1)|
Perimeter is the sum of the five edge lengths. Centroid coordinates are computed from the standard polygon centroid formula using the same ordered vertex pairs.
How to Use This Calculator
- Enter five vertices in the order you would trace the pentagon boundary.
- Use either clockwise order or counterclockwise order consistently.
- Click Calculate Area to show the result panel above the form.
- Review area, signed area, perimeter, centroid, side lengths, and the plotted shape.
- Use the CSV or PDF buttons to export the current calculation.
FAQs
1) What makes this pentagon irregular?
An irregular pentagon does not require equal sides or equal angles. This calculator accepts any five ordered vertices that form a closed five-sided polygon without self-crossing edges.
2) Why must I enter vertices in order?
The shoelace formula follows the boundary path. If points are entered out of order, edges can cross and the computed area may become incorrect or misleading.
3) Can I use negative coordinates?
Yes. Negative and decimal coordinates both work. The calculator measures the polygon from the exact numeric positions you enter on the coordinate plane.
4) What is signed area?
Signed area keeps the direction of vertex order. Counterclockwise input gives a positive signed area, while clockwise input gives a negative signed area. The absolute value is the true area.
5) Why is the centroid sometimes unavailable?
If the entered points collapse into a zero-area shape, the centroid formula becomes unstable for this polygon model. Enter a valid non-degenerate pentagon to get the centroid.
6) Does the graph change with my input?
Yes. After submission, the Plotly graph redraws the pentagon using your coordinates, closes the boundary, and keeps equal axis scaling for a realistic geometric view.
7) What do the export buttons include?
The CSV export includes vertices and calculated values. The PDF export captures the visible result panel, including the summary tables and plotted shape preview.
8) Can this calculator check self-intersections?
No. It assumes the given order traces a simple pentagon. If the edges cross, reorder the vertices before using the reported area for study or design work.