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.