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Консультация № 136836
14.05.2008, 19:56
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Здравствуйте Уважаемые Эксперты.
Вычислить площадь трапеции,параллельные стороны которой содержат 16 и 44 см а непареллельные-17см и 25см.
Вычислить площадь трапеции,параллельные стороны которой содержат 16 и 44 см а непареллельные-17см и 25см.
Обсуждение
15.05.2008, 03:45
общий
это ответ
Здравствуйте, Coolcooler1!
Проведя с концов меньшего основания трапеции на большее перепендикуляры, разобьем трапецию на три фигуры: прямоугольник со сторонами 16 и h, прямоугольный треугольник со сторонами x и h, прямоугольный треугольник со сторонами (44-16)-x=28-x и h.
Поскольку боковые стороны трапеции являются гипотенузами полученных треугольников, то имеют место соотношения: (25)^2=x^2+h^2 и (17)^2=(28-x)^2+h^2. Решая полученную систему, находим: x=20, 28-x=8, h=15.
Тогда искомая площадь трапеции S=16*15+20*15/2+8*15/2=240+150+60=450 (кв. ед.).
Ответ: 450 кв. ед.
P.S. Данное решение не назовешь математически строгим, поскольку единственность разбиения трапеции, указанного выше, не очевидна. Но это можно доказать...
Проведя с концов меньшего основания трапеции на большее перепендикуляры, разобьем трапецию на три фигуры: прямоугольник со сторонами 16 и h, прямоугольный треугольник со сторонами x и h, прямоугольный треугольник со сторонами (44-16)-x=28-x и h.
Поскольку боковые стороны трапеции являются гипотенузами полученных треугольников, то имеют место соотношения: (25)^2=x^2+h^2 и (17)^2=(28-x)^2+h^2. Решая полученную систему, находим: x=20, 28-x=8, h=15.
Тогда искомая площадь трапеции S=16*15+20*15/2+8*15/2=240+150+60=450 (кв. ед.).
Ответ: 450 кв. ед.
P.S. Данное решение не назовешь математически строгим, поскольку единственность разбиения трапеции, указанного выше, не очевидна. Но это можно доказать...
Об авторе:
Facta loquuntur.
Facta loquuntur.
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