area of triangle calculator

Triangle Area Calculator

Choose a method, enter your values, and calculate the area instantly.

How to Find the Area of a Triangle

The area of a triangle tells you how much surface is enclosed inside its three sides. Whether you're working on school math, construction planning, land measurement, or geometry practice, triangle area is one of the most useful calculations to know.

This calculator gives you two reliable methods: base and height and three sides (Heron's formula). Use whichever information you already have.

Triangle Area Formulas

1) Base and Height Formula

Area = 1/2 × base × height

This is the most common formula. If you know the triangle's base and the perpendicular height to that base, this method is direct and quick.

  • base = one side of the triangle
  • height = perpendicular distance from the opposite vertex to the base

2) Heron's Formula (Using Three Sides)

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

Use Heron's formula when you know all three side lengths but do not know the height. It works for any valid triangle: scalene, isosceles, or equilateral.

Examples

Example A: Base and Height

If base = 12 and height = 5, then:

  • Area = 1/2 × 12 × 5
  • Area = 30 square units

Example B: Three Sides

If sides are 7, 8, and 9:

  • s = (7 + 8 + 9) / 2 = 12
  • Area = √(12 × 5 × 4 × 3) = √720 ≈ 26.833
  • Area ≈ 26.833 square units

How to Use This Area of Triangle Calculator

  1. Select your preferred method.
  2. Enter the required values.
  3. Optionally enter a unit (like cm or m).
  4. Click Calculate Area.
  5. Read the result and formula breakdown instantly.

Common Mistakes to Avoid

  • Using slanted side length as height in the base-height method.
  • Mixing units (for example, base in meters and height in centimeters) without converting first.
  • Entering side lengths that do not form a valid triangle.
  • Forgetting that area is always in square units.

Where Triangle Area Is Used in Real Life

Triangle area calculations show up far beyond the classroom:

  • Architecture and roof design
  • Surveying and land division
  • Graphic design and 3D modeling
  • Engineering and physics
  • Carpentry and fabrication

Quick FAQ

Can area be negative?

No. Area represents physical space, so it is always zero or positive.

What if I only know two sides?

Two sides alone are not enough unless you also know the included angle or another related measurement. In that case, use the formula A = 1/2 ab sin(C).

What unit is the answer in?

The result is in square units. If you enter cm as the unit, your output is in cm².

Use this tool any time you need a fast, accurate triangle area result without manual algebra errors.

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