3 Sides Triangle Area Calculator
Calculate the area of any triangle using Heron's formula with all three side lengths. Free online triangle area calculator with instant results and triangle classification.
About This Calculator
The 3 Sides Triangle Area Calculator uses Heron's formula to compute the area of any triangle when only the three side lengths are known. This method works for all triangle types without needing height measurements or angles.
Heron's Formula: Area = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2 is the semiperimeter.
Frequently Asked Questions
How do you find the area of a triangle with 3 sides?
Use Heron's formula: Area = sqrt(s(s-a)(s-b)(s-c)), where a, b, c are the side lengths and s = (a+b+c)/2 is the semiperimeter. First calculate the semiperimeter, then multiply s by (s-a), (s-b), and (s-c), and take the square root of the product.
What is Heron's formula?
Heron's formula, discovered by Hero of Alexandria, calculates the area of any triangle given only the three side lengths: Area = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2. It works for all triangle types -- scalene, isosceles, and equilateral -- without needing height or angles.
Can Heron's formula be used for any triangle?
Yes, Heron's formula works for any triangle as long as the three side lengths satisfy the triangle inequality theorem (the sum of any two sides must be greater than the third side). If the sides don't form a valid triangle, the formula will produce an imaginary number because the radicand will be negative.
What is the formula for equilateral triangle area?
For an equilateral triangle with side length a, the area formula simplifies to Area = (sqrt3/4)a^2. This is derived from Heron's formula: s = 3a/2, so s(s-a)^3 = (3a/2)(a/2)^3 = (3a^4/16), and sqrt(3a^4/16) = (sqrt3/4)a^2.