Предмет: Геометрия, автор: Lazarev123a

в правильной треугольной призме ABCA1B1C1 сторонаоснования равна 4см. Точка M-середина ребра CC1. плоскость ABM образует с плоскостью основания угол 45 градусов . найдите площадь боковой поверхности призмы

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Автор ответа: Malvna

0

в основании правильный треугольник, тогда его высота по Т.Пифагора: СН=кор(4^2-2^2)=кор12=2кор3
рассмотрим треугольник МНС-прямоугольный (угол С=90), угол МНС=45, тогда угол НМС тоже 45, следовательно, трреугольник равнобедренный, тогда НС=МС=2кор3
т.к. СС1=2МС=4 кор3
тогда площадь боковой поверхности
S=Pосн*Н=(4+4+4)*4кор3=48 кор3

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