1. What is a Triangle Area Calculator (3 Sides)?

Definition: This calculator computes the area of a triangle when you know the lengths of all three sides using Heron's Formula.

Purpose: It's useful for geometry, construction, land surveying, and any application where you need to calculate triangular areas without knowing the height.

2. How Does the Calculator Work?

The calculator uses Heron's Formula:

Where:

• \( a, b, c \) — Lengths of the three sides (meters)
• \( s \) — Semi-perimeter: \( \frac{a + b + c}{2} \)
• \( Area \) — Area of the triangle (square meters)

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

3. Importance of Triangle Area Calculation

Details: Accurate area calculation is essential for material estimation, land measurement, construction planning, and geometric analysis.

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 (sum of any two sides > third side).

5. Frequently Asked Questions (FAQ)

Q1: What if my sides don't form a valid triangle?
A: The calculator will show an error if the side lengths violate the triangle inequality theorem.

Q2: Does this work for all types of triangles?
A: Yes, Heron's formula works for scalene, isosceles, and equilateral triangles.

Q3: What units should I use?
A: The calculator uses meters, but any consistent unit can be used (results will be in square units of that measurement).

Q4: How accurate is the calculation?
A: The calculation is mathematically precise, though real-world measurements may have practical limitations.

Q5: Can I use this for right triangles?
A: Yes, though for right triangles, the simpler formula (½ × base × height) may be more straightforward.