Math Geometry • Basic Shapes and Properties
Calculate the perimeter and area of any polygon: use regular polygon inputs (n + side/apothem/radius) or paste vertices (shoelace formula).
Inputs accept pi, e, sqrt(2), 1e-3. Use * for multiplication.
Example vertex formats: (0,0), 5 0, 6,4.
Pan: drag empty space • Zoom: mouse wheel/trackpad • Drag a vertex to move it.
Use the shoelace formula with vertices listed in order: A = 1/2 x |sum(xi yi+1 - xi+1 yi)|, where the last vertex connects back to the first.
Perimeter is the sum of distances between consecutive vertices, using the distance formula for each edge, including the final edge from the last vertex back to the first.
Provide the number of sides n and one measure such as side length s, apothem a, or circumradius R. Perimeter uses P = n x s, and area commonly uses A = (1/2) x P x a.
The shoelace formula assumes the vertices follow the polygon boundary in clockwise or counterclockwise order. If points are out of order, the computed area can be incorrect or represent a different shape.
Perimeter is reported in the same units as the coordinate or length inputs, while area is reported in square units. Keep units consistent across all inputs for meaningful results.