Heron's Formula Calculator

Calculate the area of a triangle using Heron's formula by entering the lengths of its sides. Ideal for students, engineers, and geometry enthusiasts.

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Data Source and Methodology

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da Wikipedia: Heron's formula.

The Formula Explained

The formula for calculating the area of a triangle when you know the lengths of all three sides is known as Heron's formula:

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

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

Glossary of Terms

How it Works: A Step-by-Step Example

For a triangle with sides 5, 6, and 7 units, the semi-perimeter \( s \) is \((5+6+7)/2 = 9\). The area is calculated as:

\[ A = \sqrt{9(9-5)(9-6)(9-7)} = \sqrt{9 \times 4 \times 3 \times 2} = \sqrt{216} \approx 14.7 \]

Frequently Asked Questions (FAQ)

What is Heron's formula used for?

Heron's formula is used to find the area of a triangle when the lengths of all three sides are known.

Can Heron's formula be used for all triangles?

Yes, as long as the side lengths form a valid triangle.

What is the semi-perimeter in Heron's formula?

The semi-perimeter is half the perimeter of the triangle.

Are there any limitations to Heron's formula?

Heron's formula requires precise side lengths and is not suitable for triangles with sides that don't form a valid shape.

How do I know if three sides form a valid triangle?

The sum of the lengths of any two sides must be greater than the length of the third side.

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