Предмет: Геометрия, автор: ivanzolo1

В правильной четырехугольной пирамиде боковое ребро равно 5 см и образует с плоскостью основания угол 45. Найдите площадь боковой поверхности.

Ответы

Автор ответа: angelinamyrzahmetova

Ответ:

SABCD -прав пирамида. ABCD - квадрат. О - т. пересечения диагоналей квадрата АС и BD.

Из прям. тр-ка SAO найдем АО:

АО = SA*sin45 = (5кор2)/2.

Из прям. тр-ка AOD найдем сторону квадрата AD:

AD= АО/sin45= 5.

Значит боковая поверхность пирамиды состоит из 4-х равносторонних тр-ов со стороной 5. ( площадь каждого - (5квкор3)/4).

Sбок = 4*(25кор3)/4 = 25кор3.

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