Step-by-step explanation:

The ratio of the circumferences of two circles is 4:5.

Let's denote the circumferences of the two circles as C1 and C2, and the radii as r1 and r2 respectively.

We know that the circumference of a circle is given by the formula C = 2πr.

So, we have the following ratios:

C1/C2 = 4/5

Substituting the formula for circumference:

(2πr1)/(2πr2) = 4/5

Simplifying:

r1/r2 = 4/5

Now, let's find the ratio of their areas. The area of a circle is given by the formula A = πr^2.

So, we have:

A1/A2 = (πr1^2)/(πr2^2)

Simplifying:

A1/A2 = (r1^2)/(r2^2)

Substituting the ratio of the radii:

A1/A2 = (4/5)^2

Simplifying further:

A1/A2 = 16/25

Therefore, the ratio of the areas of the two circles is 16:25.