Geometry Tool🔥 Popular
Triangle Calculator
Solve any triangle using side lengths, angles, or base & height. Supports SSS, SAS, ASA, and Base-Height formulas to calculate area, perimeter, angles, semi-perimeter, and altitudes.
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Interactive Triangle Calculator Workspace
Calculated Metrics
Calculated Area20.0000
Calculated using base (8) and vertical height (5).
Step-by-Step Calculation
1. Formula used: Area = 0.5 × Base × Height
2. Substitution: Area = 0.5 × 8 × 5
3. Result: Area = 20.0000
Mathematical Formula & Variables
Equation Model
Area = 0.5 × Base × Height (or Heron's Formula: √(s(s-a)(s-b)(s-c)))Finds the dimensions, angles, area, and perimeter of a triangle. Uses traditional base-height formulas or Heron's Formula (when only three side lengths are known).
Variable Definitions
| Symbol | Description |
|---|---|
| a, b, c (Sides) | The three boundary edge lengths of the triangle. |
| A, B, C (Angles) | The interior angles opposite to sides a, b, and c respectively. |
| s (Semi-perimeter) | Half of the triangle perimeter: s = (a + b + c) ÷ 2. |
| Base / Height | The horizontal bottom edge length and vertical distance to the peak. |
How to Use the Triangle Calculator
- Choose your solving method from the options tab (Base & Height, Three Sides (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA)).
- Input the known values into the corresponding form fields.
- Click calculate or watch the real-time calculations output area, perimeter, and missing sides/angles.
- Check the mathematical steps to see Law of Sines, Law of Cosines, or Heron's Formula applications.
Practical Example Calculation
Scenario Context: An architect needs to find the area of a triangular roof gable with sides measuring 6 feet, 8 feet, and 10 feet.
Step 1: Identify given values: SSS method with Side a = 6, Side b = 8, Side c = 10.
Step 2: Calculate semi-perimeter (s): s = (6 + 8 + 10) ÷ 2 = 24 ÷ 2 = 12 ft.
Step 3: Apply Heron's Formula: Area = √(s(s-a)(s-b)(s-c)) = √(12(12-6)(12-8)(12-10)) = √(12 × 6 × 4 × 2) = √576 = 24 sq ft.
Step 4: Calculate Perimeter: P = a + b + c = 6 + 8 + 10 = 24 ft.
The triangular roof gable has an area of 24.00 sq ft and a perimeter of 24.00 ft (it is a right triangle).
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