Calculate Area Of Triangle With 3 Sides

Heron's Formula:

\[ Area = \sqrt{s(s-a)(s-b)(s-c)} \] \[ \text{where } s = \frac{a+b+c}{2} \]

Area:

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1. What is Heron's Formula?

Heron's formula allows you to calculate the area of a triangle when you know the lengths of all three sides. It's useful when you don't know the height of the triangle.

2. How Does the Calculator Work?

The calculator uses Heron's formula:

\[ Area = \sqrt{s(s-a)(s-b)(s-c)} \] \[ \text{where } s = \frac{a+b+c}{2} \text{ (semi-perimeter)} \]

Where:

\( a \) — Length of side a
\( b \) — Length of side b
\( c \) — Length of side c
\( s \) — Semi-perimeter of the triangle

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

3. Importance of Triangle Area Calculation

Details: Calculating triangle area is fundamental in geometry, architecture, engineering, and various fields requiring spatial measurements.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. Values must be positive and satisfy triangle inequality (sum of any two sides > third side).

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Any consistent units (cm, m, inches, etc.). The result will be in square units of whatever you input.

Q2: Does the triangle type matter?
A: No, Heron's formula works for all triangle types (scalene, isosceles, equilateral, right-angled).

Q3: What if I get an error message?
A: Check that your side lengths satisfy the triangle inequality theorem (a + b > c, a + c > b, b + c > a).

Q4: How accurate is the calculation?
A: The calculator provides results rounded to 2 decimal places. For precise calculations, use exact values.

Q5: Can I use this for 3D triangles?
A: Heron's formula is for planar (2D) triangles. For 3D applications, you'd need additional information.