area

this is simple..

the 2nd point will be (1,0)

sorry 3rd point..

this is bcos n! pi x will be integer multiple of pi for large enough n when x is rational.. so the cos will be + or - 1 and when taken to square power, it will become +1

Again for a irrational point.. no matter how large value you take for n, the number will not be integer multiple of pi .. thus modulus of its cos will be less than 1.. very large power will take it to 0