Numarly

Triangle Area Calculator

Calculate triangle area using different methods

What is it?

This calculator finds the area of a triangle using three different methods, depending on what measurements you have: base and height, three side lengths (Heron's Formula), or vertex coordinates.

Formula

  • Base & Height: Area = ½ × Base × Height
  • Heron's Formula: Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2
  • Coordinates: Area = ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|

Formula Explanation

Base & Height works because a triangle is always exactly half of the parallelogram sharing the same base and height. Heron's Formula lets you find area from three side lengths alone using the semi-perimeter (s). The coordinate formula derives area directly from the (x, y) positions of the three vertices, useful when the triangle is plotted on a graph.

Example Calculation

Using Heron's Formula for sides 3, 4, 5: s = 6, area = √(6×3×2×1) = 6 square units.

How to Use

  1. Select the method that matches the measurements you have.
  2. Enter the required values (base/height, three sides, or three vertex coordinates).
  3. Click Calculate Area to see the result.

Benefits

  • Supports three different calculation methods for whatever data you have on hand.
  • No need to manually compute the semi-perimeter for Heron's Formula.
  • Handles coordinate geometry directly without plotting the triangle by hand.

Use Cases

  • Land surveying where only side lengths or coordinates are known.
  • Geometry and trigonometry homework or coursework.
  • Computer graphics or CAD calculations involving triangular regions.

What Your Result Means

The result is the amount of flat space enclosed by the triangle, in square units matching your input measurements. All three methods give the same area for the same triangle — they simply use different available information.

Tips

  • Use Base & Height when you can measure a perpendicular height directly.
  • Use Heron's Formula when you only know the three side lengths.
  • Use Coordinates when the triangle's vertices are plotted on a grid or graph.

Common Mistakes

  • Using a slanted side length as the "height" in the Base & Height method instead of the perpendicular height.
  • Entering side lengths for Heron's Formula that don't satisfy the triangle inequality.
  • Mixing up x and y coordinates when using the coordinates method.

FAQs

When should I use Heron's Formula?

Use Heron's Formula when you know all three side lengths of the triangle but not its height.

When should I use the coordinates method?

Use the coordinates method when you know the (x, y) position of each of the triangle's three vertices on a graph.

Do all three methods give the same result?

Yes, for the same triangle, all three methods produce the same area — they're just different ways to calculate it based on what data you have available.

What is the semi-perimeter in Heron's Formula?

The semi-perimeter (s) is half the triangle's total perimeter: s = (a + b + c) / 2, used as an intermediate step in Heron's Formula.

Can the coordinates method handle any triangle orientation?

Yes, the coordinate formula works regardless of how the triangle is rotated or positioned, since it uses absolute value to always return a positive area.

Results are in square units matching your input measurements.

Last updated: July 25, 2026