1. What is Heron's Formula for Triangle Area?

Definition: Heron's formula calculates the area of a triangle when you know the lengths of all three sides.

Purpose: It's useful when you don't know the height of the triangle but have all three side measurements.

2. How Does the Calculator Work?

The calculator uses Heron's formula:

Where:

• \( a, b, c \) — Lengths of the triangle's sides (meters)
• \( s \) — Semi-perimeter of the triangle (meters)
• \( \text{Area} \) — Area of the triangle (square meters)

Explanation: First calculate the semi-perimeter, then use it to compute the area under the square root.

3. Triangle Inequality Theorem

Details: For any valid triangle, the sum of any two sides must be greater than the third side. The calculator checks this condition.

4. Using the Calculator

Tips: Enter the lengths of all three sides in meters. All values must be positive numbers that satisfy the triangle inequality.

5. Frequently Asked Questions (FAQ)

Q1: Why use Heron's formula instead of base×height/2?
A: Heron's formula is useful when you don't know the height but have all three side measurements.

Q2: What units does this calculator use?
A: The calculator uses meters for input and square meters for the area result, but any consistent unit can be used.

Q3: What if I get an error message?
A: The error means your side lengths don't form a valid triangle. Check that the sum of any two sides is greater than the third.

Q4: How precise are the results?
A: Results are shown with 3 decimal places, but internal calculations use full precision.

Q5: Can I use this for right triangles?
A: Yes, it works for all triangle types, though for right triangles (a² + b² = c²), base×height/2 might be simpler.