Определить объём и площадь полной поверхности цилиндра, высота которого 60 см, а диаметр основания 40 см.

Решение на фотографии и ответы тоже

Площадь трапеции через диагонали  и угол между ними
S = 1/2*d₁*d₂*sin(α)
54 = 1/2*9*12*sin(α)
sin(α) = 54/54 = 1
α = 90°
Диагонали перпендикулярны, и это упрощает дело.
5² = x²+y²
a² = (9-x)²+(12-y)²
Треугольники между диагоналями и верхним и нижним основаниями подобны с коэффициентом подобия k
k = (9-x)/x
k = (12-y)/y
k = a/5
-------
(9-x)/x = (12-y)/y
9/x - 1 = 12/y - 1
3y = 4x
y = 4/3x
5² = x²+y² = x²+(4/3x)² = (9+16)/9*x²
25 = 25/9*x²
9 = x²
x = 3
y = 4/3x = 4/3*3 = 4
a² = (9-x)²+(12-y)² = (9-3)²+(12-4)² = 6²+8² = 100
a = √100 = 10

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