Determine the elevation and grade value of an unknown point K which lies along a profile vertical curve (convex in this example).

*Commonly in profile vertical curves, a parabola is applied as an approximation to circular curve, considering that for large radius values and target precision, these elements practically coincide.

^{o}C for 24 hours.

*n sides* polygonal shape with known Cartesian coordinates in the plane for all of its vertices. The main concept of the method is to divide the main polygon in *n* trapezoids
and to cross-multiply corresponding coordinates to find the area enclosing the polygon (green trapezoids), and subtract from it the surrounding trapezoids (red) to find the area
of the polygon within. It is also called the shoelace formula because of the constant cross-multiplying for the coordinates making up the polygon, like tying shoelaces. Mainly applicable in topography.

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Calculation Examples