private double GetGeometryLength(Geometry geometry)
{
    double result = 0;
    var pathGeometry = geometry as PathGeometry;
    if (pathGeometry != null)
    {
        foreach (var figure in pathGeometry.Figures)
        {
            var currentPoint = figure.StartPoint;
            foreach (var segment in figure.Segments)
            {
                var bezier = segment as BezierSegment;
                var line = segment as LineSegment;

                if (bezier != null)
                {
                    result += GetBezierLength(currentPoint, bezier.Point1, bezier.Point2, bezier.Point3);
                    currentPoint = bezier.Point3;
                }
                else if (line != null)
                {
                    result += GetLineLength(currentPoint, line.Point);
                    currentPoint = line.Point;
                }
            }
        }
    }

    return result;
}

private double GetBezierLength(Point p0, Point p1, Point p2, Point p3)
{
    double result = 0;
    Point lastPoint = p0;

    for (double t = 0.001; t <= 1; t += 0.001)
    {
        Point currentPoint;

        // Формула кубической кривой Безье
        // https://ru.wikipedia.org/wiki/Кривая_Безье
        currentPoint.X = Math.Pow(1 - t, 3) * p0.X +
            3 * t * Math.Pow(1 - t, 2) * p1.X +
            3 * t * t * (1 - t) * p2.X +
            Math.Pow(t, 3) * p3.X;

        currentPoint.Y = Math.Pow(1 - t, 3) * p0.Y +
            3 * t * Math.Pow(1 - t, 2) * p1.Y +
            3 * t * t * (1 - t) * p2.Y +
            Math.Pow(t, 3) * p3.Y;

        double dx = currentPoint.X - lastPoint.X;
        double dy = currentPoint.Y - lastPoint.Y;
        result += Math.Sqrt(dx * dx + dy * dy);
        lastPoint = currentPoint;
    }

    return result;
}

private double GetLineLength(Point p0, Point p1)
{
    double dx = p0.X - p1.X;
    double dy = p0.Y - p1.Y;
    return Math.Sqrt(dx * dx + dy * dy);
}