Triangle Area Calculator Formula

Understand the math behind the triangle area calculator. Each variable explained with a worked example.

Use the Triangle Area Calculator

Formulas Used

Area

area = 0.5 * base * height

Perimeter Note

perimeter_note = base * height

Variables

VariableDescriptionDefault
baseBase10
heightHeight6

How It Works

How to Calculate Triangle Area

Formula

A = ½ × base × height

Where:

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

    • This formula works for all triangles — the height must be perpendicular to the base.

    Worked Example

    Find the area of a triangle with base 10 and height 6.

    base = 10height = 6
    1. 01A = ½ × 10 × 6
    2. 02= ½ × 60
    3. 03= 30

    When to Use This Formula

    • Calculating the area of a triangular plot of land for real estate valuations, property tax assessments, or fencing estimates.
    • Determining the material needed for triangular architectural features — gable ends, sail shades, decorative panels, or custom-cut tiles.
    • Solving structural engineering problems where triangular load distributions or cross-sections determine stress and deflection.
    • Computing areas of irregular polygons by decomposing them into triangles and summing the individual triangle areas.
    • Working through geometry or trigonometry coursework involving triangle area in proofs, coordinate geometry, or optimization problems.

    Common Mistakes to Avoid

    • Using a slant side instead of the perpendicular height — the formula A = ½bh requires h to be the vertical distance from the base to the opposite vertex, not the length of one of the other sides (unless the triangle is a right triangle and the sides are the legs).
    • Forgetting the ½ factor — computing b × h instead of ½ × b × h doubles the actual area. This is an easy slip, especially under time pressure on exams.
    • Choosing a base and height that don't correspond — the height must be perpendicular to whichever side you designate as the base. Picking the height relative to a different side produces a wrong answer.
    • Not recognizing when to use Heron's formula — if you know all three sides but not the height, A = ½bh cannot be applied directly. Use Heron's formula A = √(s(s-a)(s-b)(s-c)) where s is the semi-perimeter.

    Frequently Asked Questions

    How do you find the area of a triangle?

    The simplest formula is A = ½ × base × height. The height must be perpendicular to the base.

    What if I do not know the height?

    If you know all three sides, use Heron's formula: A = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2. If you know two sides and the included angle, use A = ½ × a × b × sin(C).

    Learn More

    Guide

    How to Calculate Area of Shapes - Complete Guide

    Learn how to calculate the area of common shapes including rectangles, triangles, circles, trapezoids, parallelograms, and ellipses with formulas and examples.

    Ready to run the numbers?

    Open Triangle Area Calculator