Triangle Area Using 3 Sides

Heron's Formula:

\[ Area = \sqrt{s(s-a)(s-b)(s-c)} \]

where \( s = \frac{a + b + c}{2} \) (semi-perimeter)

Area:

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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 three side lengths of a triangle.

2. How Does the Calculator Work?

The calculator uses Heron's formula:

\[ Area = \sqrt{s(s-a)(s-b)(s-c)} \]

where \( s = \frac{a + b + c}{2} \) (semi-perimeter)

Where:

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

Explanation: First calculate the semi-perimeter, then use it in the 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 positive and satisfy the triangle inequality theorem.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: The calculator uses meters, but any consistent unit can be used - the result will be in square units of that measurement.

Q2: Why does my input give an error?
A: The three side lengths must satisfy the triangle inequality: sum of any two sides must be greater than the third side.

Q3: Can I use this for right triangles?
A: Yes, but for right triangles, using ½×base×height might be simpler.

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

Q5: What if my triangle is degenerate?
A: The calculator will show an error as degenerate triangles (where a+b=c) have zero area.