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Консультация № 197693
04.02.2020, 23:03
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Основанием прямой призмы АВСА1В1С1 является равнобедренный прямоугольный треугольник АВС (угол АВС= 90 градусов). Боковая грань АА1В1В - квадрат, площадь которого равна 36см2. Вычислите объём призмы АВСА1В1С1.
Основанием прямой призмы АВСА1В1С1 является равнобедренный прямоугольный треугольник АВС (угол АВС= 90 градусов). Боковая грань АА1В1В - квадрат, площадь которого равна 36см2. Вычислите объём призмы АВСА1В1С1.
Обсуждение
09.02.2020, 19:56
общий
это ответ
Здравствуйте, svrvsvrv!
Поскольку площадь боковой грани - квадрата AA1B1B равна 36 см2, то AB = AA1 = [$8730$]36 = 6 см, где AA1 - высота призмы, а AB - катет основания ABC. Поскольку ABC - равнобедренный треугольник, то BC = AB = 6 см, S[$916$]ABC = 62/2 = 18 см2 и объём призмы равен 18[$183$]6 = 108 см3.
Поскольку площадь боковой грани - квадрата AA1B1B равна 36 см2, то AB = AA1 = [$8730$]36 = 6 см, где AA1 - высота призмы, а AB - катет основания ABC. Поскольку ABC - равнобедренный треугольник, то BC = AB = 6 см, S[$916$]ABC = 62/2 = 18 см2 и объём призмы равен 18[$183$]6 = 108 см3.
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