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 height measurements but know all side lengths of a triangle.

2. How Does the Calculator Work?

The calculator uses Heron's formula:

Where:

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

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, architecture, engineering, and various construction projects.

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 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: 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: Can I use this for right triangles?
A: Yes, Heron's formula works for all types of triangles, including right triangles.

Q4: How accurate is the result?
A: The calculator provides results with 3 decimal places, but actual accuracy depends on your input measurements.

Q5: What if my sides don't form a valid triangle?
A: The calculator will display an error message if the input values violate the triangle inequality theorem.