Final answer:
The area of the table not covered by the four placemats is 2268 square inches.
Step-by-step explanation:
First, let's find the dimensions of the table. Since the four placemats each have a perimeter of 36 inches, the length of each side of a placemat is 36 inches divided by 4, which is 9 inches. Since the table is square and has a side length of 4 feet, which is equal to 48 inches, the area of the table is 48 inches multiplied by 48 inches, which is 2304 square inches. The area covered by the four placemats is equal to the total length of the sides of the four placemats, which is 9 inches multiplied by 4, which is 36 inches. So, the area of the table not covered by the placemats is equal to the total area of the table minus the area covered by the placemats, which is 2304 square inches minus 36 square inches, which is 2268 square inches.