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We start with the circular table and determine the radius of the circle formed by the table.
The area is given as 1256 square inches.
the formula for the area of a circle is
Since the diameter of a circle equals 2 times the radius, then the diameter of the table = 39.98985957 inches.
Each leaf has a width of 12 inches and a length of the diameter of the circle which would be a length of 39.98985957 inches
The area of each of the leafs will be 12 inches * 39.98985957 inches = 479.8783148 square inches.
Since the new square inches is 2696 and the old square inches is 1256, then the number of additional square inches of area is equal to 2696 - 1256 = 1440 square inches.
1440 / 479.8783148 = 3.000760725 additional leafs required.
Since you can only add leafs in integral amounts, the answer would be 3 leafs.
3 leafs would give you an area of 1439.634944 additional square inches on top of 1256 square inches which would give you a total area of 2695.634944 square inches.
This is close to the area you were looking for but not right on.
If you round to the nearest integer, however, then the answer would be correct.
3 leafs added to the existing area of the table would become 2696 square inches.