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Консультация № 196336
09.09.2019, 15:44
0.00 руб.
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Дана прямая треугольная призма ABCA1B1C1. В основании - равнобедренный прямоугольный треугольник (угол АВС равен 90 градусов). СС1=2см. Площадь боковой поверхности призмы равна 12+6×корень из 2 см2. F принадлежит AA1. Плоскость FВС образует с плоскостью основания угол в 30 градусов. Найти площадь сечения FВС.
Дана прямая треугольная призма ABCA1B1C1. В основании - равнобедренный прямоугольный треугольник (угол АВС равен 90 градусов). СС1=2см. Площадь боковой поверхности призмы равна 12+6×корень из 2 см2. F принадлежит AA1. Плоскость FВС образует с плоскостью основания угол в 30 градусов. Найти площадь сечения FВС.
Обсуждение
12.09.2019, 14:45
общий
это ответ
Здравствуйте, svrvsvrv!
Имеем
PABC -- периметр основания призмы;
Sбок=PABC*|CC1| -- площадь боковой поверхности призмы [1, с. 16];
PABC=Sбок/|CC1|=(12+6[$8730$]2)/2=6+3[$8730$]2 (см);
|AB|=|BC|, |AC|=[$8730$](|AB|2+|BC|2)=|AB|[$8730$]2;
PABC=|AB|+|BC|+|AC|=(2+[$8730$]2)|AB|=6+3[$8730$]2[$8658$]|AB|=3 (см);
SABC=|AB|*|BC|/2=|AB|2/2=9/2 (см2) -- площадь основания призмы;
SABC=SFBC*cos(30[$186$])[$8658$]SFBC=SABC/cos(30[$186$])=(9/2)/([$8730$]3/2)=3[$8730$]3[$8776$]5,20 (см2) -- площадь сечения FBC (здесь мы воспользовались теоремой о площади проекции многоугольника [2, с. 92]).
Литература
1. Цыпкин А. Г., Цыпкин Г. Г. Математические формулы. -- М.: Наука, 1985. -- 128 с.
2. Геометрия. 10 -- 11 классы / А. Д. Александров, А. Л. Вернер, В. И. Рыжик. -- М.: Просвещение, 2014. -- 255 с.
Имеем
PABC -- периметр основания призмы;
Sбок=PABC*|CC1| -- площадь боковой поверхности призмы [1, с. 16];
PABC=Sбок/|CC1|=(12+6[$8730$]2)/2=6+3[$8730$]2 (см);
|AB|=|BC|, |AC|=[$8730$](|AB|2+|BC|2)=|AB|[$8730$]2;
PABC=|AB|+|BC|+|AC|=(2+[$8730$]2)|AB|=6+3[$8730$]2[$8658$]|AB|=3 (см);
SABC=|AB|*|BC|/2=|AB|2/2=9/2 (см2) -- площадь основания призмы;
SABC=SFBC*cos(30[$186$])[$8658$]SFBC=SABC/cos(30[$186$])=(9/2)/([$8730$]3/2)=3[$8730$]3[$8776$]5,20 (см2) -- площадь сечения FBC (здесь мы воспользовались теоремой о площади проекции многоугольника [2, с. 92]).
Литература
1. Цыпкин А. Г., Цыпкин Г. Г. Математические формулы. -- М.: Наука, 1985. -- 128 с.
2. Геометрия. 10 -- 11 классы / А. Д. Александров, А. Л. Вернер, В. И. Рыжик. -- М.: Просвещение, 2014. -- 255 с.
5
Большое спасибо за помощь.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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