Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 3, July 2023

A man owns a square shaped patio with an area of 64 square meters. At each corner there is an antique lantern.

Since he likes to spend time on it, he wants to increase the size of his patio. However, it should keep its square shape and no lantern should be rebuilt or removed. Since this is where the sunlight lasts the longest, he also does not want to build the patio elsewhere in his yard. The center of the patio should still be the same distance from all the lanterns. What is the maximum area he can extend the patio to in this way?