What Is a Scalene Triangle?
A scalene triangle is a triangle in which all three sides have different lengths, and consequently all three interior angles differ. Because no side or angle is equal, you cannot use the simple base × height ÷ 2 shortcut unless you happen to know a base and its perpendicular height. When you only know the three side lengths, Heron's formula is the cleanest way to find the area — and this calculator does it for you instantly.
How to Use This Calculator
Enter the three side lengths a, b and c in any consistent unit (cm, m, inches, etc.). The calculator first checks the triangle inequality — the sum of any two sides must be greater than the third — to ensure the triangle is valid. It then computes the semi-perimeter and applies Heron's formula. The result is the area in square units, along with the perimeter and semi-perimeter for reference.
The Formula Explained
Heron's formula computes area directly from the side lengths. First find the semi-perimeter: \(s = (a + b + c) / 2\). Then the area is \(\sqrt{s(s-a)(s-b)(s-c)}\). This works for any triangle — scalene, isosceles or equilateral — making it a versatile tool whenever the three sides are known but the height is not.
$$A = \sqrt{s\,(s-a)\,(s-b)\,(s-c)}$$
Worked Example
Suppose a triangle has sides a = 7, b = 8 and c = 9. The semi-perimeter is \(s = (7 + 8 + 9) / 2 = 12\). Then the area
$$A = \sqrt{12 \times (12-7) \times (12-8) \times (12-9)} = \sqrt{12 \times 5 \times 4 \times 3} = \sqrt{720} \approx 26.83 \text{ square units.}$$FAQ
Does this only work for scalene triangles? No — Heron's formula works for any valid triangle. It is simply most useful for scalene triangles where no shortcut applies.
What if the sides don't form a triangle? If the longest side is greater than or equal to the sum of the other two, the triangle inequality fails and the area is reported as 0, since no such triangle exists.
What units does the answer use? The area is in square units of whatever length unit you entered. If you used centimetres, the area is in square centimetres.
