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ABCD is a regular tetrahedron with each edge of length L. What is the perpendicular distance from any vertex to the opposite face?
- sqrt(2/3) * L
- sqrt(3/2) * L
- (2/3) * L²
- (1/sqrt(3)) * L
Correct answer: sqrt(2/3) * L
Solution
For a regular tetrahedron with edge L, the height (vertex to opposite face) is h = L * sqrt(2/3). This follows from the centroid of the base equilateral triangle being at distance L/sqrt(3) from each vertex, and applying Pythagoras: h = sqrt(L² - L²/3) = L*sqrt(2/3).
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