|x|+|y|=5 represents four lines in the four quadrants

x+y=5
x-y=5
-x-y=5
x-y=0

forming a square with side 10.

Area = 100

IMO D (50)

You get four different equations:
1. y=-x+5
2. y=-x-5
3. y=x-5
4. y=x+5

These form a square with the y-axis as its diagonal of length 10.
This diagonal divides the square into two isoceles triangles of the form 45-45-90. The ratio of the sides in this kind of triangle is x : x : x*sqroot2.

Therefore x*sqroot2=10
x=10/sqroot2

Now we can solve for the area:
x^2=(10/sqroot2)^2=100/2=50

oops..I agree