Предмет: Геометрия, автор: kwh

найдите площадь прямоугольной трапеции у которой две меньшей стороны равны 6 см а большой угол равен 135 градусов

Ответы

Автор ответа: RastaRV

ABCD-прямоуг. трап.
BA=6cм
BC=6см
уг.A=90гр
уг.B=90гр
уг.C=135гр

Найдем угол CDA
уг.CDA=360-(135+180)=45гр
Достроим до прямоугольника.
ABKC-прямоуг.
уг.K=90гр
треуг.CKD-равноб. т.к. BK-разв.уг.=180гр, а значит 180-135=45гр (уг.KCD)
уг.KDC=180-(90+45)=45гр.
CK=KD
KD=BA (прямоуг.) =6см
BK=AD=6+6=12cм
S(ABCZ)=6^2=36см^2 -квадрат.
Sтреуг.CZD=(6^2)/2=18см^2
Sтрап.=18+36=54cм^2
Ответ: 54см^2

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