Which grill pan has more cooking area?

Pictured above are two Lodge grill pans. One is round, and one is square.

The round grill pan is 11 1/4 inches* in diameter; The square grill pan is 10 1/2 inches.

*Lodge recently changed the size of its round grill pan to 10 1/4 inches, but this article refers to the 11 1/4 inch pan.

So, many would assume that the round grill pan has more cooking area, right?

WRONG! Yes, I'm a nerd, and I pulled out a calculator.

The area of a circle is 3.14 times the radius, squared.

The radius is half the diameter, 5.625 inches.

5.625 * 5.625 = 31.64; 31.64 * 3.14 = 99.35 square inches of cooking area.

The area of a square is length times width. 10.5 * 10.5 = 110.25 square inches of cooking area.

See, I had been considering getting a round grill pan and selling the square one, since I wanted more cooking area-- but actually, I'd have LESS cooking area.

I have since obtained a round grill pan, and found that, as burgers are round, three medium sized burgers can comfortably fit in this pan.

In the square grill pan, three burgers CAN fit, but it's a bit more crowded-- even though there's technically more cooking area.

It's because of the shape of the burgers, vs. the shape of the pan.

Now, is that clear as mud?