The perimeter of triangle b is 6 times greater than the perimeter of
triangle a. the area of triangle b is how many times greater than the
area of triangle a?

a. 36 times greater
b. 6 times greater
c. 3 times greater
d. 1.5 times greater

This is the concept of scale factors, to answer the question we proceed as follows;
linear scale factor=[Perimeter of B]/[Perimeter of A]=6
also:
Area scale factor=[linear scale factor]^2
but;
linear scale factor=6
hence;
Area scale factor=6^2=36
therefore we conclude that the area of triangle B is 36 time than that of triangle A. The answer is:
A] 36 times greater.