Any polygon — by corner points
Area and perimeter, with the formula worked through and a drawing to scale.
Result
- Area
- 120 sq ft
- = 120 sq ft · 11.1484 m²
- Perimeter
- 42.4222 ft
- = 42.4222 ft · 12.9303 m
The working
Area: A = ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|
Perimeter: P = Σ √((xᵢ₊₁ − xᵢ)² + (yᵢ₊₁ − yᵢ)²)
A = ½ × |240| = 120 P = sum of the 5 edge lengths = 42.4222
Values in feet; areas in sq ft.
About the any polygon — by corner points
For any straight-sided shape — an irregular lot, a room with odd corners. Walk round the outline and note each corner as x,y from a fixed start point; the shoelace formula does the rest. Corners must be in order around the edge.
Every formula on this site is explained step by step in Learn: area and perimeter.
Other shapes
Square Rectangle Parallelogram Rhombus Trapezoid (trapezium) Kite Triangle — three sides Triangle — base and height Right triangle Isosceles triangle Equilateral triangle Triangle — two sides and the angle between Circle Semicircle Quarter circle Sector (pie slice) Circular segment (arch) Ring (annulus) Ellipse (oval) Regular polygon (pentagon, hexagon, octagon…) L-shape