1. What is Heron's Formula?

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 have the height of the triangle but know all three side lengths.

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
• \( \text{Area} \) — Area in square meters

Explanation: First calculate the semi-perimeter, then use it in the main formula to find the area.

3. Importance of Triangle Area Calculation

Details: Calculating triangle areas is fundamental in geometry, construction, land surveying, and various engineering applications.

4. Using the Calculator

Tips: Enter the lengths of all three sides in meters. All values must be > 0 and must satisfy the triangle inequality theorem.

5. Frequently Asked Questions (FAQ)

Q1: What is the triangle inequality theorem?
A: It states that the sum of any two sides must be greater than the third side (a+b>c, a+c>b, b+c>a).

Q2: Can I use this for any type of triangle?
A: Yes, Heron's formula works for all triangle types (scalene, isosceles, equilateral, right-angled).

Q3: What units does this calculator use?
A: The calculator uses meters for input and square meters for output, but any consistent unit can be used.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact, though practical measurements may have precision limitations.

Q5: What if I get an error message?
A: The error means your side lengths cannot form a triangle. Check your measurements and try again.