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Area (Heron's)
14.6969
Formel
## 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**
Lösungsbeispiel
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
Häufig Gestellte Fragen
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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