Given equation of lines are: 

y - x = 0 ..........1

x + y = 0 .........2

x - k = 0 ..........3

From euqation 1 and 2 , we get

x =0 , y= 0

From euqation 2 and 3 , we get

x =k , y= -k

From euqation 1 and 3 , we get

x =k , y= k

Now the points are (0,0), (k,-k), (k,k)

Now if three points (x₁ ,y₁ ), (x₂ ,y₂ ), (x₃ ,y₃ ) are given then area of triangle is

      (1/2)*|x₁ (y₂ -y₃ ) + x₂ (y₃ -y₁ ) + x₃ (y₁ - y₂ )|

   = (1/2)*|0(-k-k) + k(k-0) + k(0+k)|

   = (1/2)*|k² + k² |

   = 2k² /2

   = k²

So area of triangle is k²