The sequence `(1)/(sqrt(3)), (1)/(sqrt(3)+sqrt(2)), (1)/(sqrt(3) + 2 sqrt(2))` form an ........ .

Explanation

Area of qudrilateral AbCD is maximum when area of ACD is maximum. Area of triangle ACD.
`Delta_1=(1)/(2)||{:(3/sqrt2,,sqrt2,,),(3/sqrt2,,-sqrt2,,),(3sintheta,,2costheta,,),(3/sqrt2,,sqrt2,,):}||`
`=|-3sqrt(2)costheta+3sqrt(2)sintheta|`
`therefore Delta_1("max")=6`, when`theta=(7pi)/(4)` (as `theta epsilon(3pi//2,2pi`))
Maximum area is 12 sq.units (as ABCD is a rectangle).