Thanks for the query.

Let us consider that the sides of the polygons are in the ratio of 1 : k

Then their areas will be in the ratio 1 : k^2

Their perimeter will be in the ratio 1 : k

Therefore, 1 / k = 12 / 18

k = 3 / 2

Hence Area of polygon 1 + Area of polygon 2

= Area of polygon 1 + k^2 * Area of polygon 1 (since the Areas are in the ratio of 1 : k^2)

=> Area of polygon 1 + (9 / 4)* Area of polygon 1 = 65

**Solving we get Area of polygon 1 >>> 20 sq units**

and Area of polygon 2 >>> 20*(9 / 4) = 45 sq. units