let

r1 = the radius of the first circle

C1 = 2 r1 pi the circumference of the first circle

r2 = the radius of the second circle

C2 = 2 r2 pi the circumference of the second circle

the circumference of two circles are in the ratio 4:5:

C1 : C2 = 4 : 5

C1 / C2 = 4 / 5

2 r1 pi / 2 r2 pi = 4 / 5

r1 / r2 = 4 / 5

(r1^2)/(r2^2) = 4^2 / 5^2

(r1^2 pi)/(r2^2 pi) = 16/25

the ratio of their areas is 16 : 25.