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Triangle Area & Perimeter Calculator

Use our free online Triangle Area Calculator to perform fast, accurate calculations with instant formulas, step-by-step arithmetic, and verified reference benchmarks.

Triangle Area Calculator

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How to Calculate: The Triangle Area Calculator Formula

Standard: Area = 0.5 × Base × Height | Heron's: Area = √[ s(s - a)(s - b)(s - c) ] where s = (a + b + c)/2

Calculates the enclosed 2D surface area of right, equilateral, isosceles, and scalene triangles.

Step-by-Step Calculation Guide

  1. Input base length and perpendicular vertical height (or 3 side lengths).
  2. Apply geometric area formula.
  3. Review total triangle area.
  4. Inspect perimeter.

Practical Triangle Area Calculator Examples

Base & Height Example

Base = 10 cm, Height = 6 cm.

Area = 0.5 × 10 × 6 = 30 cm².
Area: 30 cm².
Heron's Formula (Sides: 7, 8, 9)

Sides: a=7, b=8, c=9. Semi-perimeter s = (7+8+9)/2 = 12.

Area = √[12(12-7)(12-8)(12-9)] = √[12 × 5 × 4 × 3] = √720 = 26.83.
Area: 26.83 sq units.

Triangle Area Formulas by Known Information

Official reference values and benchmark classifications based on standard institutional guidelines.

Known ParametersArea FormulaBest Triangle Types
Base (b) & Height (h)Area = 0.5 × b × hRight & standard triangles with known altitude
Three Sides (a, b, c)Area = √[s(s-a)(s-b)(s-c)]Scalene triangles with unknown height
Two Sides & Angle (SAS)Area = 0.5 × a × b × sin(C)Oblique surveying & navigation
Equilateral Side (s)Area = (√3 / 4) × s²Equal three-sided geometric figures

Frequently Asked Questions about Triangle Area Calculator

How do you find the height of a triangle?

Height is the perpendicular distance from any chosen base to the opposite apex vertex (h = 2 × Area / base).

What is Heron's formula?

Heron's formula calculates the area of any triangle using only the lengths of its three sides without needing angles or altitude.

Can any 3 numbers form a triangle?

No. The Triangle Inequality Theorem dictates that the sum of any two side lengths must be strictly greater than the third side (a + b > c).

What is the area of a right triangle?

For a right triangle, the two perpendicular legs serve directly as the base and height: Area = (leg1 × leg2) / 2.

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