if area is 20 units along y-z plane then why we take area vector as 20i

Area vector is defined in the direction perpendicular to the plane in which the surface actually lies. So, here in this case, the surface lies in the y-z plane and hence, area vector would be defined in the plane perpendicular to y and z i.e. (y x z) = i plane. 

 

Also, the magnitude of the area vector is equal to the area of the surface. 

Hence area vector = 20i.