Applications of Area and Perimeter

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Waffles. They're way better than pancakes. Fight me irl if you disagree. They even have pockets for the syrup...

But are those pockets optimal?

Suppose we have a standard Eggo waffle. It has a diameter of 95 mm and a height of 12 mm. Both sides of the waffle are symmetrical and the square pockets have a depth of 3 mm. Furthermore, assume the syrup perfectly fills the square pockets of one side and no more.

The square pockets must satisfy the following constraints:

• The square pockets must form a grid of congruent squares
• The walls of the pockets must be at least 1 mm thick.
• The square pockets, along with the irregular (non-square) pockets at the boundary of the waffle, must be able to contain at least 16 mL of syrup. (Note: 1 mL = 1 cm$^3$.)
• The waffle must have rotational symmetry.

Under these constraints, an optimal waffle would minimize the sizes of the square pockets. That way, there are lots of pockets, and the syrup doesn't spill all over while eating the waffle.