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Math • Triangle Area Calculator

Triangle Area Calculator

Calculate the area, hypotenuse, and angles of a right triangle from its two legs.

Hypotenuse (c)
5.000
√(a² + b²)
Angle ∠A
36.87°
arctan(a / b)
Angle ∠B
53.13°
90° - ∠A
Triangle Area
6.00
½ × a × b
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Calculation Guide & Reference

Right Triangle Area Mathematics

Triangle area calculator computes the area, hypotenuse, and angles of a right triangle from its two legs.

Standardized Mathematical Formula
Area = (1/2) × a × b

For a right triangle, the area is half the product of the two legs (the sides forming the right angle) — equivalent to the standard base × height ÷ 2 formula, since the legs serve as base and height.

Variables:
a:First leg (adjacent to the right angle)
b:Second leg (adjacent to the right angle)
How It Works (Step-by-Step)
  • 1Enter the lengths of the two legs of the right triangle.
  • 2View the area, the hypotenuse, and both non-right angles.
Real-World Numerical Example
A 3-4-5 Right Triangle

A right triangle has legs of length 3 and 4 (the classic 3-4-5 triangle).

•Area: (1/2) × 3 × 4 = 6 square units.
•Hypotenuse: √(3² + 4²) = √25 = 5.
Result: The triangle has an area of 6 square units and a hypotenuse of 5.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

Area = (1/2) × leg₁ × leg₂ — half the product of the two legs forming the right angle.

Use Area = (1/2) × base × height, where height is measured perpendicular to the chosen base — or use Heron's formula if you only know the three side lengths.

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