三角形计算器(进阶) — 公式

Triangle Area via Heron's Formula

Formula

s = (a + b + c) / 2 (semi-perimeter)

Area = sqrt(s × (s-a) × (s-b) × (s-c))

Heron's formula computes the area of any triangle when you know all three side lengths, without needing height or angles.

Inradius

The inradius (radius of the inscribed circle) is: r = Area / s

计算示例

Triangle with sides 5, 6, 7.

  1. s = (5+6+7)/2 = 9
  2. Area = √(9 × 4 × 3 × 2) = √216 ≈ 14.6969
  3. Inradius = 14.6969 / 9 ≈ 1.6330