Triangle Area Calculator
Triangle Area Calculator
When you know all three side lengths of a triangle but not its height, Heron's formula lets you find the area directly - no need to identify a base and drop a perpendicular. Enter the three sides, and this calculator computes the semi-perimeter, the area, and the perimeter, along with a diagram and the full step-by-step working.
- Heron's formula: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (a+b+c)/2 - for sides 5, 6, 7, s = 9 and the area is √(9×4×3×2) ≈ 14.70.
- The three sides must satisfy the triangle inequality (each side shorter than the sum of the other two), or no such triangle exists - the calculator returns an area of 0 in that case.
- This method works for any triangle - scalene, isosceles, or equilateral - and is often faster than the base × height formula when only the three sides are known.
How do I find the area of a triangle with 3 sides?
Use Heron's formula: first find the semi-perimeter s = (a+b+c)/2, then Area = √(s(s-a)(s-b)(s-c)). For sides 5, 6, 7: s = 9, Area = √(9×4×3×2) ≈ 14.70.
What if the three sides can't form a triangle?
If one side is longer than or equal to the sum of the other two, the sides can't form a closed triangle, and the formula under the square root becomes zero or negative - the calculator shows an area of 0.
Triangle Area Calculator
When you know all three side lengths of a triangle but not its height, Heron's formula lets you find the area directly - no need to identify a base and drop a perpendicular. Enter the three sides, and this calculator computes the semi-perimeter, the area, and the perimeter, along with a diagram and the full step-by-step working.
- Heron's formula: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (a+b+c)/2 - for sides 5, 6, 7, s = 9 and the area is √(9×4×3×2) ≈ 14.70.
- The three sides must satisfy the triangle inequality (each side shorter than the sum of the other two), or no such triangle exists - the calculator returns an area of 0 in that case.
- This method works for any triangle - scalene, isosceles, or equilateral - and is often faster than the base × height formula when only the three sides are known.
How do I find the area of a triangle with 3 sides?
Use Heron's formula: first find the semi-perimeter s = (a+b+c)/2, then Area = √(s(s-a)(s-b)(s-c)). For sides 5, 6, 7: s = 9, Area = √(9×4×3×2) ≈ 14.70.
What if the three sides can't form a triangle?
If one side is longer than or equal to the sum of the other two, the sides can't form a closed triangle, and the formula under the square root becomes zero or negative - the calculator shows an area of 0.