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Exercise 2.In a regular hexagonal pyramid MABCDEF in which the side edges equal 4 and the edges of the base equal 1, calculate the distance from the middle of edge BC to face EMD.Solution. In a regular hexagon
and
. Since МО is the altitude of the pyramid, then in right-angled triangle MOD we find
In right-angled triangle MDN we find the apothem of face DME:
Planes
and
are perpendicular; therefore altitude OH of triangle MON is perpendicular to plane DME. In right-angled triangle MON we find
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