Parabolic Conic Section

Geometry Level 4

A cone of altitude 20 and an apex angle of \( \theta_0 = \tan^{-1}(\frac{1}{2}) \) (This is the angle between the axis of the cone and its lateral surface), is cut by a plane oriented in such a way to produce a parabolic section. If the lower point of the cut is half the slant height away from the apex, then find the area of the parabolic section (shaded yellow) to 2 decimal places.

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