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Motivation In Teaching Mathematics

Table 4:

Exercise 1. In a regular hexagonal prism ABCDEFA1B1C1D1E1F1 whose edges equal 1, calculate the distance from point А to plane A1B1C.Solution. Plane АА1Е is perpendicular to plane А1В1С which contains straight line FC, and these two planes intersect along line A1G. Therefore the length of altitude АH in triangle АA1G is the solution to the exercise. In right-angled triangle ADE we calculate A E = A D 2 - E D 2 = 3 , consequently A G = 3 2 . Then in right-angled triangle АGA1 we calculate G A 1 = 3 4 + 1 = 7 2 , and the end result is A H = A G ∙ A A 1 G A 1 = 3 7 . The answer: 3 7 .
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