An Online calculator to calculate the area of a triangle formed by three lines as shown in the figure below.
Let the three lines be given by the equations:
\[L_1: a_1 x + b_1 y = c_1\] \[L_2: a_2 x + b_2 y = c_2\] \[L_3: a_3 x + b_3 y = c_3\]
The intersection point \(A\) of \(L_1\) and \(L_2\) is found using Cramer's rule:
\[x_A = \frac{\begin{vmatrix} c_1 & b_1 \\ c_2 & b_2 \end{vmatrix}}{\begin{vmatrix} a_1 & b_1 \\ a_2 & b_2 \end{vmatrix}}, \quad y_A = \frac{\begin{vmatrix} a_1 & c_1 \\ a_2 & c_2 \end{vmatrix}}{\begin{vmatrix} a_1 & b_1 \\ a_2 & b_2 \end{vmatrix}}\]
Similarly for points \(B\) (\(L_2 \cap L_3\)) and \(C\) (\(L_1 \cap L_3\)).
The area is then calculated using Heron's formula:
\[s = \frac{AB + BC + CA}{2}\] \[\text{Area} = \sqrt{s(s-AB)(s-BC)(s-CA)}\]
Enter coefficients for three lines in the form \(ax + by = c\)
Tip: For vertical lines \(x = k\), set \(a=1, b=0, c=k\). For horizontal lines \(y = k\), set \(a=0, b=1, c=k\).