Area of Quadrilateral Calculator
Find the area of any quadrilateral with this area of a quadrilateral calculator.
Working
| Semi-perimeter s | 10 |
| Area (Heron) | √(s(s−a)(s−b)(s−c)) = 14.142136 |
| Height on side a | 2 × area ÷ a = 5.656854 |
| Inradius | area ÷ s = 1.414214 |
| Circumradius | abc ÷ 4·area = 4.772971 |
| Angle sum | 180° (always 180°) |
The formula
split into two triangles along a diagonal
Four sides do not fix a quadrilateral
Unlike a triangle, a quadrilateral with four given sides can flex — the same four lengths enclose different areas depending on the angles. That is why a diagonal is needed: it locks the shape into two rigid triangles.
Area scales with the square
Double every length in a flat shape and the area quadruples; triple them and it grows ninefold. Perimeter, being a length, scales in step with the sides. That mismatch is why bigger shapes enclose proportionally more area per unit of edge — and why a circle, having no corners at all, encloses the most area for a given perimeter of any shape.
Units
Whatever unit you enter, the area comes out in that unit squared and the perimeter in the unit itself. The calculator is unit-agnostic — enter centimetres and read cm and cm², or feet and read ft and ft². Just do not mix units between fields.