Geometry Tool

Triangle Calculator

Calculate Area and Perimeter using SSS (Heron's Formula).

Σ The Formula

Area = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2 | Perimeter = a + b + c

Real World Examples

Equilateral
Sides: 5, 5, 5 → Area=10.83, Perimeter=15
Scalene
Sides: 3, 4, 5 → Area=6, Perimeter=12
Isosceles
Sides: 6, 6, 8 → Area=17.89, Perimeter=20
Right Triangle
Sides: 5, 12, 13 → Area=30, Perimeter=30

# About This Calculator

Heron's formula is a powerful method for calculating the area of any triangle when you know all three side lengths, without needing to know angles or height. Named after Hero of Alexandria (1st century AD), this formula works for all triangle types: equilateral, isosceles, scalene, and right triangles.

Triangles are fundamental shapes in geometry with countless real-world applications: construction (roof trusses, bridges), surveying (land measurement), navigation (triangulation), and engineering (structural analysis). Understanding triangle properties is essential for many STEM fields.

The formula uses the semi-perimeter (s = (a+b+c)/2) and calculates area as √(s(s-a)(s-b)(s-c)). This elegant approach only requires the three side lengths, making it perfect for situations where measuring height or angles is impractical. The triangle inequality (sum of any two sides must exceed the third) ensures valid triangles.

This calculator automatically validates that your sides form a valid triangle, computes both area and perimeter, and shows step-by-step calculations. It's ideal for homework, construction planning, land surveying, or any situation requiring precise triangle measurements.

How To Use

  1. Enter lengths for Side A, B, and C.
  2. Click Calculate.

Frequently Asked Questions

What types of triangles can this calculate?+

All types! Equilateral (all sides equal), isosceles (two sides equal), scalene (all sides different), and right triangles. As long as the three sides satisfy the triangle inequality (sum of any two sides > third side), Heron's formula works.

Why does it say 'Invalid Triangle'?+

The triangle inequality was violated: the sum of any two sides must be greater than the third side. For example, sides 1, 2, 10 don't form a triangle because 1+2 < 10. Check your measurements - one side might be too long.

How is this different from base × height ÷ 2?+

Both give the same area, but Heron's formula doesn't require knowing the height. Base × height ÷ 2 needs a perpendicular height measurement, which can be difficult. Heron's only needs the three side lengths, making it more practical for many situations.

Can I use this for right triangles?+

Yes! For right triangles, you can verify using both methods. A 3-4-5 triangle: Heron's gives area = 6. Using base × height: (3 × 4) ÷ 2 = 6. Same result! Heron's works for all triangles, including right triangles.

What's the semi-perimeter and why is it used?+

Semi-perimeter (s) is half the perimeter: s = (a+b+c)/2. It's used in Heron's formula to simplify the calculation. For sides 3, 4, 5: s = 6. Then area = √(6×3×2×1) = 6. It's a mathematical convenience that makes the formula elegant.

Is Triangle Calculator free to use?+

Yes, Triangle Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

Heron's formula is a powerful method for calculating the area of any triangle when you know all three side lengths, without needing to know angles or height. Named after Hero of Alexandria (1st century AD), this formula works for all triangle types: equilateral, isosceles, scalene, and right triangles.

Triangles are fundamental shapes in geometry with countless real-world applications: construction (roof trusses, bridges), surveying (land measurement), navigation (triangulation), and engineering (structural analysis). Understanding triangle properties is essential for many STEM fields.

The formula uses the semi-perimeter (s = (a+b+c)/2) and calculates area as √(s(s-a)(s-b)(s-c)). This elegant approach only requires the three side lengths, making it perfect for situations where measuring height or angles is impractical. The triangle inequality (sum of any two sides must exceed the third) ensures valid triangles.

This calculator automatically validates that your sides form a valid triangle, computes both area and perimeter, and shows step-by-step calculations. It's ideal for homework, construction planning, land surveying, or any situation requiring precise triangle measurements.

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