Area of a Triangle (Heron's Formula)

📊 intermediate

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

Calculates the area of a triangle when only the lengths of the three sides are known.

Variables & Units

$s$

Semi-perimeter ($[a+b+c]/2$)

Unit: Length

$a, b, c$

Side lengths

Unit: Length

Key Information

📐 Derived From

Trigonometric Law of Cosines and Area formula.

💡 Example

Area of triangle with sides $7, 24, 25$.

🔧 Applications

Land surveying and architectural drafting.

⚠️ Constraints

Sides must satisfy the triangle inequality.

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