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🔺 Triangle Area Calculator

Calculate triangle area using multiple methods

Triangle Area Formulas

Base and Height

Area = (base × height) / 2

Most common. Works when you know the base and perpendicular height.

Heron's Formula (3 sides)

s = (a + b + c) / 2
Area = √[s(s-a)(s-b)(s-c)]

Use when you know all three side lengths.

Two Sides and Included Angle (SAS)

Area = (a × b × sin(C)) / 2

When you know two sides and the angle between them.

Coordinates (Shoelace Formula)

Area = |x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| / 2

When you know the coordinates of all three vertices.

Quick Examples

Base & Height
10 × 6 / 2
30 sq units
Right Triangle
3 × 4 / 2
6 sq units
3-4-5 Triangle
Heron (3,4,5)
6 sq units
Equilateral (s=6)
(6²√3)/4
15.59 sq units
SAS: 5,7,60°
5×7×sin(60°)/2
15.16 sq units
Coords (0,0)(4,0)(2,3)
Shoelace
6 sq units

Real-World Applications

🏗️ Construction

  • • Roof truss calculations
  • • Land surveying
  • • Foundation layouts
  • • Material estimation

🎨 Design

  • • Graphic layouts
  • • Pattern making
  • • Textile design
  • • Interior spaces

📐 Engineering

  • • Structural analysis
  • • Load distribution
  • • CAD design
  • • Bridge design

🌍 Geography

  • • Land area measurement
  • • Property boundaries
  • • Map calculations
  • • GIS applications

How to Use This Calculator

1

Enter Your Values

Input the required values in the calculator fields above. Make sure all inputs are valid numbers.

2

Click Calculate

Press the "Calculate" button to perform the calculation and see your results.

3

Review Results

Review the calculated results displayed below. Use these values for your needs.

About Triangle Area Calculator

The Triangle Area Calculator is a useful tool for calculating triangle area values. This calculator helps you quickly and accurately determine the results you need for your calculations.

When to Use This Calculator

  • Quick Calculations: Get instant results without manual computation
  • Accuracy: Ensure precise calculations every time
  • Planning: Use for project planning and estimation
  • Verification: Double-check your manual calculations

Why Use Our Calculator?

  • ✅ Instant Results: Get accurate calculations immediately
  • ✅ Easy to Use: Simple interface for all skill levels
  • ✅ 100% Free: No registration or payment required
  • ✅ Mobile Friendly: Works on all devices
  • ✅ Accurate: Precise mathematical calculations

Tips for Best Results

  • Double-Check Inputs: Verify all values before calculating
  • Use Valid Numbers: Ensure inputs are valid numbers
  • Review Results: Check results for reasonableness
  • Clear and Retry: Clear inputs if you need to recalculate
Frequently Asked Questions

Which formula should I use?

Use base×height/2 if you know those. Use Heron's if you know all three sides. Use SAS if you know two sides and the angle between. Use coordinates if you have vertex positions.

Why divide by 2 in triangle area?

A triangle is half of a rectangle/parallelogram. Rectangle area = base × height. Triangle = (base × height) / 2 since it's half the rectangle.

Can any three lengths form a triangle?

No! Triangle Inequality: sum of any two sides must be greater than the third side. Example: 2, 3, 10 cannot form a triangle (2+3 10).

What is semiperimeter in Heron's formula?

Semiperimeter (s) is half the perimeter: s = (a+b+c)/2. It simplifies Heron's formula and represents the "average" side length.

How do I find the height if I don't know it?

Use Pythagorean theorem for right triangles, or use one of the other formulas (Heron's or SAS) if you know different measurements.