One circular table has a diameter of 8 ft. and another circular table has a diameter of 12 ft. how much greater is the area of the larger table?

If the ratio of the lengths is a:b then the areas are in the ratio of the square of these, namely a2:b2

The lengths are in the ratio 8:12 ⇒ 2:3

Therefore the areas are in the ratio 22:32 ⇒ 4:9

So the area of the larger table is 9/4 = 21/4 = 2.25 times the area of the smaller table.