Heron's Formula
Finds the area of a triangle using only the lengths of its three sides.
別名: Heron's formula, Hero's formula, ヘロン
数式
S = sqrt(s(s-a)(s-b)(s-c)), s = (a+b+c)/2
変数
| S | Area of the triangle (m²) |
|---|---|
| a | Length of side a (m) |
| b | Length of side b (m) |
| c | Length of side c (m) |
| s | Semiperimeter (m) |
計算例
a = 3、b = 4、c = 5 の三角形の面積を求めよ。
s = \dfrac{3+4+5}{2} = 6
S = \sqrt{6(6-3)(6-4)(6-5)} = \sqrt{6 \cdot 3 \cdot 2 \cdot 1}
S = \sqrt{36} = 6