Perimeter of a Triangle Calculator
Calculate triangle perimeter using different methods: three sides (SSS), two sides and angle (SAS), or two angles and side (ASA)
Calculate Triangle Perimeter
SSS
Three sides given
SAS
Two sides + angle
ASA
Two angles + side
Triangle Perimeter Results
Method used: SSS - Three sides given
Formula: Perimeter = a + b + c
Example Calculation
Garden Fence Example (SAS Method)
Problem: Calculate fence needed for triangular garden
Given: Two sides a = 8 ft, b = 6 ft, angle γ = 75°
Step 1: Find third side using law of cosines
c = √(8² + 6² - 2×8×6×cos(75°)) = √(64 + 36 - 96×0.259) = √75.136 = 8.67 ft
Step 2: Calculate perimeter
Perimeter = 8 + 6 + 8.67 = 22.67 ft
Triangle Types
Scalene
All sides different lengths
Isosceles
Two sides equal length
Equilateral
All sides equal length
Quick Tips
Triangle inequality: sum of any two sides > third side
Use SSS when all three sides are known
Use SAS when two sides and included angle are known
Use ASA when two angles and included side are known
Understanding Triangle Perimeter
What is Perimeter?
The perimeter of a triangle is the total distance around its edges. It's calculated by adding the lengths of all three sides together. This measurement is useful in real-world applications like fencing, framing, or any project where you need to know the total length around a triangular shape.
Calculation Methods
- •SSS: Simply add all three known sides
- •SAS: Use law of cosines to find third side, then add
- •ASA: Use law of sines to find missing sides, then add
Mathematical Formulas
Basic Formula (SSS):
P = a + b + c
Law of Cosines (SAS):
c = √(a² + b² - 2ab·cos(γ))
Law of Sines (ASA):
a/sin(α) = b/sin(β) = c/sin(γ)