Очень нужно пож. 60б Основания прямого параллелепипеда - параллелограмм со сторонами 15 см и 25 см и диагональю 20 см. Меньшее диагональное сечение параллелепипед - квадрат. чертеж, дано, решение, ответ

ответ: V=6000см³; Sсеч=400см²; Sосн=300см²; Sбок.пов=1600см²;

Sпол=2200см², высота=20см

Объяснение: найдём площадь основания параллелепипеда. Диагональ ВД делит основание на 2 равных треугольника, в которых известны стороны. Рассмотрим полученный ∆АВД. В нём АВ=15см, ВД=20см, АД=25см. Найдём периметр этого треугольника:

Р=15+20+25=60см; р/2=60/2=30см.

Найдём площадь ∆АВД по формуле:

S∆АВД=√((р(р-АВ)(р-ВД)(р-АД))=

=√((30(30-15)(30-20)(30-25))=

=√(30×15×10×5)=√22500=150см²

S∆АВД=S∆ВСД=150см²

Зная площади 2-х треугольников, найдём площадь основания АВСД:

Sосн=150×2=300см².

Так как диагональное сечение параллелепипеда - квадрат, то

ВД=В1Д1=ВВ1=ДД1=20см

Площадь диагонального сечения:

Sсеч=20²=400см²

ВВ1, ДД1, АА1, СС1 также являются высотами параллелепипеда, поэтому мы може найти площадь каждой боковой грани по формуле прямоугольника:

Sбок.гр.АА1ДД1=АД×АА1=25×20=500см²

Sбок.гр.АА1ДД1=Sбок.грВВ1СС1=500см²

Sбок.гр.АА1В1В=Sбок.гр.ДД1С1С=

=15×20=300см²

Так как каждой грани по 2 найдём площадь боковой поверхности параллелепипеда:

Sбок.пов=500×2+300×2=1000+600=

=1600см²

Площадь полной поверхности параллелепипеда- это сумма всех площадей его граней:

Sпол=Sбок.пов.+ S2-х.осн=1600+300×2=

=1600+600=2200см²

Теперь найдём объем параллелепипеда по формуле: V=Sосн×АА1=300×20=6000см³

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1. S = ½×(4+8)×5 = ½×6×5 = 3×5 = 15 см².

2. S=150, h=S:(½×(a+b)) = 150:(½×(9+11)) = 150:(½×20) = 150:10 = 15 см.

3. Пусть высота будет BH(нужно отметить Н на рисунке). Проведём высоту из точки С, будет она СЕ. Т.к. трапеция равнобедренная, то АН=DE. AH=BH=4 см, ведь угол А=45°, угол Н=90°, соответственно угол В=45° и треугольникк АВН равнобедренный. Из этого, AD=4+5+4 = 13 см.

Найдём площадь: S=½×(5+13)×4 = ½×18×4 = 9×4 = 36 см².

4. Пусть одна часть будет х, тогда BC=3x, AD=4x.

S=½×(3x+4x)×5 = ½×7x×5 = 3,5x×5 = 17,5x -> 17,5x = 35.

x=2 см.

AD=4x = 4×2 = 8 см.