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Math

Area of a Triangle Calculator.

Calculates the area of a triangle given its base and height, or using Heron's formula with three side lengths.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Enter the base length of the triangle.

  2. 2

    Enter the height (perpendicular distance from base to opposite vertex).

  3. 3

    Multiply base by height.

  4. 4

    Divide the product by 2 to get the area.

0.5 * base * height

Frequently asked questions

What if I only know the three side lengths?

Use Heron's formula: s = (a+b+c)/2, area = sqrt(s(s-a)(s-b)(s-c)). This calculator uses base and height, but you can compute the height from sides if needed.

Can the base and height be in any unit?

Yes, as long as they are in the same unit. The area will be in square units of that unit.

What if the base or height is zero?

The area will be zero, which is correct for a degenerate triangle.

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Results

Formula checked

Area

25sq units

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Estimate for general guidance only — verify important decisions with an appropriate professional.

How it works

Calculates the area of a triangle given its base and height, or using Heron's formula with three side lengths.

  1. Enter the base length of the triangle.
  2. Enter the height (perpendicular distance from base to opposite vertex).
  3. Multiply base by height.
  4. Divide the product by 2 to get the area.

Formulas

The math behind this calculator, written out so you can verify the result.

Standard formula

Area = (base × height) / 2

The area of a triangle is half the product of its base and the perpendicular height.

Example:

Input: base = 10, height = 5

Calculation: (10 × 5) / 2

Result: 25 square units

Real-world use cases

Where this calculation shows up in everyday life.

Construction and carpentry

Calculate the area of triangular roof sections or gable ends to estimate materials.

Example: A gable with base 20 ft and height 8 ft has area 80 sq ft.

Land surveying

Determine the area of triangular plots of land when base and height are known.

Example: A triangular lot with base 100 m and height 60 m has area 3000 m².

Geometry homework

Quickly verify answers for triangle area problems.

Example: Base 6 cm, height 4 cm gives area 12 cm².

Tips and common mistakes

Tips

  • Ensure the height is perpendicular to the base, not a slanted side.
  • Use consistent units for base and height.
  • For right triangles, the two legs can serve as base and height.
  • Double-check your measurements to avoid errors.

Common Mistakes to Avoid

  • Using a slanted side as the height.
  • Forgetting to divide by 2.
  • Mixing units (e.g., base in meters, height in centimeters).

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.