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A polygon area calculator computes the area of any polygon given its vertices using the Shoelace formula (Gauss's area formula), which works for any non-self-intersecting polygon.
Guia passo a passo
- 1Shoelace formula: A = ½|Σ(xᵢ×yᵢ₊₁ − xᵢ₊₁×yᵢ)|
- 2List vertices in order (clockwise or counterclockwise)
- 3Works for any shape: triangle, quadrilateral, irregular polygon
- 4Perimeter: sum of distances between consecutive vertices
Exemplos resolvidos
Entrada
Triangle vertices: (0,0), (4,0), (2,3)
Resultado
A = ½|0×0−4×0 + 4×3−2×0 + 2×0−0×3| = ½|0+12+0| = 6 sq units
Perguntas frequentes
What's the apothem?
Distance from centre of regular polygon to midpoint of side. Used for area calculation of regular shapes.
How do I find area of irregular polygon?
Divide into triangles, calculate each, sum. Or use shoelace formula if coordinates known.
What's Heron's formula?
For triangle with sides a,b,c: A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. No height needed.