Scalene Triangle Area Calculator

Depending on what information you have available, this calculator applies one of several geometric formulas. If you know the base and perpendicular height, it uses the standard formula: Area = 0.5 * base * height. When given two sides and the angle between them (Side-Angle-Side), it applies trigonometric principles: Area = 0.5 * a * b * sin(C). If you only know the lengths of all three sides (a, b, and c), the calculator leverages Heron's Formula: Area = 0.25 * sqrt((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c)). Finally, if you know one side and two adjacent angles (Angle-Side-Angle), it determines the remaining dimensions using the Law of Sines before computing the total area.

Let's find the area of a scalene triangle where all three sides are known: side a = 3 inches, side b = 5 inches, and side c = 7 inches. First, find the semi-perimeter (s) by adding the sides together and dividing by two: s = (3 + 5 + 7) / 2 = 7.5 inches. Next, substitute these values into Heron's formula: Area = 0.25 * sqrt( (7.5 + 5 + 7) * (-3 + 5 + 7) * (3 - 5 + 7) * (3 + 5 - 7) ). This simplifies to Area = 0.25 * sqrt( 15 * 9 * 5 * 1 ). Multiplying those terms inside the root gives sqrt(675), which is approximately 25.9807. Finally, multiply by 0.25 to yield a final area of approximately 6.495 square inches.

Always double-check your input units to ensure they are consistent across all sides and angles before computing. When using side lengths alone for Heron's formula, verify that the triangle inequality theorem holds true—meaning the sum of any two side lengths must strictly exceed the length of the third side. If you are measuring angles, confirm whether your calculator input is set to degrees or radians to avoid severe computation errors.