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🔺 Triangle Calculator

Calculate triangle area, perimeter, angles, and type using three input modes: base & height, three sides (Heron's formula), or two sides and an included angle (SAS).

Area = ½ × base × height. Enter the base and perpendicular height.

Triangle Formulas

Base & Height: Area = ½ × b × h
Heron's (SSS): s = (a+b+c)/2  |  Area = √(s(s−a)(s−b)(s−c))
SAS: Area = ½ × a × b × sin(C)
Law of Cosines: cos A = (b²+c²−a²) / (2bc)

Worked Example — Sides 3, 4, 5 (SSS)

s = (3 + 4 + 5) / 2 = 6
Area = √(6 × 3 × 2 × 1) = √36 = 6
Perimeter = 3 + 4 + 5 = 12
Angle A = arccos((16+25−9)/(2×4×5)) = arccos(0.8) ≈ 36.87°
Angle B = arccos((9+25−16)/(2×3×5)) = arccos(0.6) ≈ 53.13°
Angle C = 90° — Right Triangle

Frequently Asked Questions

The most common formula is Area = ½ × base × height, where height is the perpendicular distance from the base to the opposite vertex. When only sides are known, use Heron's formula.

Heron's formula computes a triangle's area using only its three side lengths. First calculate the semi-perimeter: s = (a+b+c)/2. Then Area = √(s(s−a)(s−b)(s−c)). It works for any triangle.

Use the law of cosines when you have SSS or SAS — it directly finds the missing side or angle. Use the law of sines (a/sin A = b/sin B) when you have AAS or ASA, as it is algebraically simpler in those cases.

By sides: Equilateral (all three sides equal, all angles 60°), Isosceles (two sides equal), Scalene (all sides different). By angles: Right (one 90° angle), Acute (all angles < 90°), Obtuse (one angle > 90°).

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