Çözüldü Two Dimensional Coordinate Geometry

On the Cartesian plane, if the lines L1: y - (√3)x + 7 = 0 and L2: (√3)y - x + 11 = 0 intersect at a point K, and two points A and B are selected on these lines so that |AK| = 6 units and |BK| = 4 units, what is the area of the triangle ABK?
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Rewriting the lines in the slope-intercept form (y = mx + n), their slopes are m1 = √3 and m2 = 1 / √3, the tangent value of the angle between these lines;
tan(θ) = (√3 - 1 / √3) / [ 1 + (√3)·(1 / √3) ] = 1 / √3 ⇒ sin(θ) = 1 / [ (√3)^2 + 1^2 ]^0,5 = 1 / 2
Area(ΔABK) = (1 / 2)·|AK|·|BK|·sin(θ) = (1 / 2)·6·4·(1 / 2) = 6 unit^2