免费三角形计算器(进阶)
根据多种参数计算三角形的面积、周长和各项属性。
Area (Heron's)
14.6969
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.
- 01s = (5+6+7)/2 = 9
- 02Area = √(9 × 4 × 3 × 2) = √216 ≈ 14.6969
- 03Inradius = 14.6969 / 9 ≈ 1.6330
常见问题
What is Heron's formula?
Heron's formula calculates the area of a triangle from the lengths of its three sides, using the semi-perimeter. No angles or heights are needed.
When does Heron's formula not work?
The three sides must satisfy the triangle inequality (each side must be less than the sum of the other two). If not, the three lengths cannot form a triangle.
What is the inradius?
The inradius is the radius of the largest circle that fits entirely inside the triangle (the inscribed circle). It equals the area divided by the semi-perimeter.
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