Scalene Triangle Calculator

A scalene triangle is a triangle where all sides have different lengths and all angles have different measures. This calculator helps you determine the area and perimeter of a scalene triangle using the side lengths.

Calculation Formula

For a scalene triangle with sides \( a \), \( b \), and \( c \), the semi-perimeter \( s \) is calculated as:
\[ s = \frac{a + b + c}{2} \]

The area \( A \) is then calculated using Heron's formula:
\[ A = \sqrt{s(s - a)(s - b)(s - c)} \]

The perimeter \( P \) is simply:
\[ P = a + b + c \]

Example Calculation

Given sides \( a = 5 \) units, \( b = 7 \) units, and \( c = 8 \) units:

• \( s = \frac{5 + 7 + 8}{2} = 10 \) units
• Area: \( A = \sqrt{10 \times (10 - 5) \times (10 - 7) \times (10 - 8)} = \sqrt{10 \times 5 \times 3 \times 2} = \sqrt{300} \approx 17.32 \) square units
• Perimeter: \( P = 5 + 7 + 8 = 20 \) units

FAQs

1. What makes a triangle scalene?
   A scalene triangle has all sides and angles different from each other.

2. How do I know if three sides form a valid scalene triangle?
   The sum of the lengths of any two sides must be greater than the length of the remaining side. Also, no sides should be equal.

This calculator simplifies determining key properties of a scalene triangle for your math and geometry needs.