Geometry
Triangle Area Calculator
Compute triangle area from base, height, or all three sides. Calculate the area of any triangle using base-height, Heron's formula, or trigonometric methods with full step-by-step working.
Live Vector System
Core Dimensions
Analytic Metrics
Surface Area
78.54
Perimeter
31.416
Mathematical Verification
Our engine utilizes double-precision floating-point arithmetic for geometric derivations. For triangles, we implement Heron's Theorem with strict validation to ensure the triangle inequality principle is maintained.
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Solution Methodology
01
Choose Input Mode
Select base-height, three sides (Heron), or two sides with included angle (SAS).
02
Compute Semi-perimeter
For Heron's method: s = (a + b + c) / 2.
03
Apply Formula
Evaluate the selected formula and simplify to get area in square units.
Common Questions
How do you find the area of a triangle with three sides?
Use Heron's formula. First compute the semi-perimeter s = (a+b+c)/2, then Area = √(s(s−a)(s−b)(s−c)). This works for any triangle when you know all three side lengths but not the height.
What is the easiest triangle area formula?
The simplest is Area = ½ × base × height. You need the base length and the perpendicular height from that base to the opposite vertex. If those two values are known, no trigonometry or Heron's formula is required.