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Консультация № 150329
12.11.2008, 15:40
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В правильной четырехугольной пирамиде площадь боковой поверхности равна 16 корней из 2, а площадь основания 4. Найдите высоту пирамиды.
Обсуждение
12.11.2008, 16:00
общий
это ответ
Здравствуйте, Sweetlovellygirl!
Сторона основания a=[$8730$]4=2
Площадь боковой грани S=16[$8730$]2/4=4[$8730$]2
Высота боковой грани h=2S/a=2*4[$8730$]2/2=4[$8730$]2
Высота боковой грани является гипотенузой прямоугольного треугольника, катетами которого являются высота пирамиды и половина стороны основания (вернее равный ей отрезок)
Отсюда, по теореме Пифагора H=[$8730$](h2-(a/2)2)=[$8730$](32-1)=[$8730$]31
Сторона основания a=[$8730$]4=2
Площадь боковой грани S=16[$8730$]2/4=4[$8730$]2
Высота боковой грани h=2S/a=2*4[$8730$]2/2=4[$8730$]2
Высота боковой грани является гипотенузой прямоугольного треугольника, катетами которого являются высота пирамиды и половина стороны основания (вернее равный ей отрезок)
Отсюда, по теореме Пифагора H=[$8730$](h2-(a/2)2)=[$8730$](32-1)=[$8730$]31
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