How high ?!
Polyhedron - has the bottom rectangle measuring and top rectangle measuring . The two rectangles are aligned, with the longer edges parallel to the -axis, and the shorter edges parallel to -axis, and their centers lying on the vertical -axis with a vertical separation of .
Now the planes connecting the two rectangles are extended, so that they form the polyhedron - on top of rectangle . How high above the plane of rectangle are points and ? (they are at the same elevation)
The answer is 56.
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1 solution
Taking a horizontal cross section of polyhedron E F G H − I J at elevation z , it will be a rectangle having dimensions L ( z ) × W ( z )
The length L ( z ) = 5 6 + h ( 3 2 − 5 6 ) z = 5 6 − z , and the width W ( z ) = 3 6 + h 2 4 − 3 6 z = 3 6 − 2 1 z
Since L ( z ) vanishes before W ( z ) (for a less value of z ), it follows that point I and J are at an elevation of z = 5 6 .