Let's call the original radius of the circle "r".

When the radius is increased by 6%, the new radius becomes r + (r * 0.06) = 1.06r.

The area of a circle is given by the formula:

A = π * r^2

So, the original area of the circle would be:

A = π * r^2

And the new area of the circle would be:

A' = π * (1.06r)^2

To find the increase in area, we can subtract the original area from the new area:

A' - A = π * (1.06r)^2 - π * r^2
A' - A = π * (1.06^2) * r^2 - π * r^2
A' - A = π * (1.1236) * r^2 - π * r^2

We can simplify the expression to get:

A' - A = π * (1.1236 - 1) * r^2
A' - A = π * 0.1236 * r^2

So, the increase in area is proportional to the square of the increase in radius. To find the percentage increase in area, we would need to know the original radius and calculate the increase as a fraction of the original area. But in general, increasing the radius by 6% leads to an increase in area of approximately 12.36% (calculated as 0.1236 * 100).