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fundamental definition for centroid

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The asking problem:
Show that when the distance h is selected to maximize the distance Y from line BB' to the centroid of the shaded area, we also have Y=h.
Note: The Y is relating to the centroid Y of the area. The drawing is in word97 format for PC and not for MAC.

My problem is I don't know how can I demonstrate this. Can you explain to me how??

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Solution Preview

Use the fundamental definition for centroid.
Let S(a-b) [f(y)dy] denote the definite integral of function f(y) from y=a to y=b.

Centroid = Y = S(0-b) [y*A(y) dy ] / S(0-b) [ A(y) dy]

Divide area A into A1 which consists of ...

Solution Summary

A fundamental definition for centroid is embodied. The solution shows how to maximize the distance of a centroid shaded.