Problem Solving

A cylinder has a base with a circumference of meters and an equilateral triangle inscribed on the interior side of the base. A marker is dropped into the tank with an equal probability of landing on any point on the base. If the probability of the marker landing inside the triangle is , what is the length of a side of the triangle?

a)3*((2pi)^1/2)(square root over 2*pi)
b)3*((3pi)^1/2)(square root over 3*pi)
c)10*pi^1/2 (square root over pi)
d)10*((3pi)^1/2)(square root over 3*pi)
e)20*pi

Could you please put this problem directly from the source. Quite uneasy to understand the options. well the approach should be,

Calculate the area of triangle.

then the probability will be area of triangle/area of circle.

Isn't this question really time consuming? Should I expect this kind of questions on GMAT?