In an isoceles triangle OAB , O is the origin and OA=OB=6 . The equation of the side AB is x-y+1=0 Then the area of the triangle is

Options

A. `2sqrt(21)`
B. `sqrt(142)`
C. `sqrt((142)/(2))`
D. `sqrt((71)/(2))`

Answer

D

Explanation

Let D be the midpoint of AB.
`OD=(1)/(sqrt(2))`
`AD = sqrt(6^(2)-OD^(2)) = sqrt(36-(1)/(2)) = sqrt(17)/(2)`
`therefore "Area of triangle" = (1)/(2) xx AB xx OD = sqrt((17)/(2)) xx sqrt((1)/(2))= sqrt(71)/(2)`