A projectile touches 4 verices of a regular hexagon of side length 10√3. Find its time of flight.

let projectile is projected at a distance a from the corner of the base so its range must be

 R = a+10√3 + a

      = 2a +10√3

so 2a + 10√3 = V² sin2b/2g  

 or  g/v²cos²b = sinb/(2a+10√3)  ....................1

select first two corner point of hexagon ,if the projectile pass through these point then by symmetry it will also pass through oteher two ppoints

 points are ( a-10√3cos60 , 10√3sin60)   and  (a,20√3sin60)

use the general equation

y =x tanb - gx²/2v²cos²b

put above these two point and put the value of g/v²cos²b = sinb/(2a+10√3) 

then u will get 2 equation in a and tanb  

solve it  and then easly u can get desired result