The square footage of an irregular triangle is found with Heron’s formula from its three sides. Compute s = (a+b+c)/2, then Area = √[s(s−a)(s−b)(s−c)].
Our triangle area guide and irregular acreage guide show how to apply this to awkward triangles and real land plots.
How to Calculate the Square Footage of an Irregular Triangle
An irregular triangle is simply a triangle whose three sides are all different lengths — the typical shape of a corner lot or a triangular section of a yard bounded by three fences. The reason this gets its own calculator is practical: out in a yard you can measure the three sides easily with a tape, but you almost never have a clean “base and height” with a perpendicular drop. Fortunately, three sides are all you need.
Three sides are enough: Heron's formula
Unlike a four-sided shape, a triangle is completely fixed by its three side lengths — there is only one triangle (and one area) for a given set of sides. The area comes from Heron's formula:
Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c) ⁄ 2
Here a, b and c are the three sides and s is the semi-perimeter (half the perimeter). The calculator does the arithmetic; you just supply the three lengths.
Measuring a triangular lot
Walk the boundary and measure each of the three sides in turn, keeping the tape taut and flat along each fence or edge. Label them in any order — A, B and C — because Heron's formula gives the same area regardless of order. The one rule the three lengths must obey is the triangle inequality: any two sides added together must be longer than the third. If they are not, the lengths cannot form a triangle, and the calculator will say so, which is a useful sign to re-check a measurement.
Worked example
Consider a triangular garden bounded by fences of 30, 40 and 50 feet.
Semi-perimeter s = (30 + 40 + 50) ⁄ 2 = 60. Area = √(60 × 30 × 20 × 10) = √360,000 = 600 square feet. (These are 3-4-5 proportions, so it is a right triangle — a handy check, since ½ × 30 × 40 also equals 600.)
Where irregular triangles appear
- Corner lots: Properties where two roads meet at an angle often leave a triangular parcel.
- Yard sections: Triangular flower beds, lawn wedges and side-yard strips.
- Gable ends and roof faces: Many roof planes and wall gables are triangles measured by their edges.
- Leftover plots: The odd triangular remainder when a rectangular area is divided diagonally.
Related shape calculators
If you do have a clean base and perpendicular height, the base-and-height triangle calculator is quicker. For a four-sided plot, use the irregular quadrilateral calculator, and for a house gable specifically, the gabled wall calculator combines a triangle with a rectangle.