By Zencalcy Editorial TeamLast reviewed About us
Three ways to one answer: ½ × base × height for the classic case, Heron's formula when you know all three sides, or the shoelace formula when you have vertex coordinates. Pick the tab that matches your data.
Base×height, Heron's formula, or vertex coordinates (shoelace).
½·b·h | √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 | shoelace from coordinates
| Symbol | Meaning |
|---|---|
| b, h | Base and height |
| a, b, c | Three side lengths (must satisfy triangle inequality) |
| (x,y) | Vertex coordinates |
Base 10, height 6 → 30. Sides 3-4-5 → s = 6, area = √(6·3·2·1) = 6. Vertices (0,0),(4,0),(0,3) → 6.
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Base/height when available (simplest); Heron when you only know side lengths; coordinates when working from a grid or map.
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Content updated: September 2026