Triangle incicle, area and angles
Calculates parameter of a triangle using Herons formula.
This function calculates the area, angles and incircle of a triangle according to Heron's theorem. To calculate, enter the lengths of all three sides. Then click on Calculate. Please note that any two sides together must be longer than the third.
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Formulas for calculating the area of a triangle
Calculation from three given side lengths
The mathematician Heron's theorem describes a mathematical formula for calculating the area of a triangle from given three side lengths.
Area
\(\displaystyle A = \sqrt{s · (s-a) · (s-b) ·(s-c)} \)
Half of the perimeter
\(\displaystyle s = \frac{ a + b + c}{2} \)
Alternative formulas
\(\displaystyle A = \frac{1}{4} · \sqrt{(a+b+c)·(-a+b+c)·(a-b+c)·(a+b-c)} \)
\(\displaystyle A = \frac{1}{4} · \sqrt{4·a^2·b^2-(a^2+b^2-c^2)} \)
Incircle radius
\(\displaystyle r = \frac{\sqrt{s·(s-a)·(s-b)·(s-c)}}{s}\)
Incircle area
\(\displaystyle r = r^2 ·π\)
Angle α
\(\displaystyle α = arccos\left(\frac{b^2+c^2-a^2}{2bc} \right)\)
Angle β
\(\displaystyle β = arccos\left(\frac{a^2+c^2-b^2}{2ac} \right)\)
Angle γ
\(\displaystyle γ = arccos\left(\frac{a^2+b^2-c^2}{2ab} \right)\)
Height
\(\displaystyle h = b·sin(γ)\)
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