Предмет: Математика, автор: asdf1fnf

СРОЧНО В основании прямой призмы лежит ромб; диагонали призмы составляют с плоскостью основания углы 300 и 600. Высота призмы равна 6 см. Найти объем призмы (Желательно, либо прислать фото решения, либо прислать подробную разборку задания, чтобы я мог переписать)

Ответы

Автор ответа: galiuddbf68
1

Ответ:

Пусть АВСД А1В1С1Д1 -данная призма. Проведём в ромбе-основании диагонали. Тогда угол АСА1 =30 и АА1=6

и угол САА1 =90. Поэтому АС = 6 / tg30 = 6 : (√3/3) = 6√3

В тр-ке ВДД1 угол ВДД1=90, угол ДВД1 =60 и ДД1=6 тогда ВД = 6 / tg60 = 6 / √3=2√3

Площадь ромба равна половине произведения его диагоналей и равна= 0,5*6√3*2√3= 18

Тогда объём равен= 18*6 =108 куб см


asdf1fnf: это делается через дано?
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