∑ Mathematics LabPolygons · v4.0.4

MATHEMATICS LAB · GEOMETRY

Study of Polygons

Construct regular and irregular polygons, drag vertices and see how sides, angles, diagonals, perimeter and area change. Compare quadrilaterals and geometric constructions.

Vertices follow the boundary in order. Polygons must be simple (no crossing edges). Lengths are measured in arbitrary units (u), areas in u².

1. Define the polygon

Coordinates and parameters

Drag the center to move the figure, or a vertex to change radius and orientation while preserving regularity.

Examples:

2. Interactive construction

Cartesian plane · equal axis scale
Regular polygon
Drag vertices to edit the polygon.

Drag the vertices to change the shape. In regular mode, you can also drag the center O. Use the mouse wheel or + and − to zoom, and drag the background to pan. “Fit” centers the entire figure.

Outline and vertices Internal triangles Diagonals Altitudes and feet Axes of symmetry Circles, apothem and center

3. Understanding the construction

4. Results

Updated instantly

5. Explained calculations

MathJax formulas and substitutions

What you can study

Regular polygons

Apothem, circumradius, circles, central angles, side lengths and areas.

Irregular polygons

Free vertices, perimeter, area by the shoelace formula, reflex angles, diagonals and internal triangulation.

Quadrilaterals

Rectangles, squares, rhombi, parallelograms, trapezoids and kites, with diagonals, altitudes and symmetry axes.

Coordinates and results are numerical: tolerances classify nearly regular shapes. Incircles and circumcircles are shown only for regular polygons. Concave polygons are triangulated internally; some diagonals may extend outside the polygon.