Вопрос школьника по предмету Геометрия
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Диагональ BD трапеции ABCD равна большему основанию AD этой трапеции и перпендикулярна к нему. Найдите площадь трапеции, если AB= 3 корня из 2 см, угол С = 60 градусам.
Ответ учителя по предмету Геометрия
∆ ABD — прямоугольный, BD=АD=AB•sin45°=3 см.
∠BDA=90°, ⇒∠ DBC=90° как накрестлежащий.
∆ BCD — прямоугольный. ⇒
ВC=BD/tg60°=3/√3=√3
S ABCD=(3+√3)•3:2= ≈7,098 см
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