Question

Geometry area question. Please help!

Answer 1

You can calculate polygon area with only apothem OR side length.

apothem only
area = apothem^2 * 6 * tan (180/6)
area = 10.4^2 * 6 * 0.57735
area = 108.16 * 3.4641
area = 374.677056 square yards

side length only
area = 6 * 12^2 * / 4*tan(30)
area = 864 / 4 * 0.57735
area = 864 / 2.3094
area = 374.1231488698 square yards

If apothem and side length were given with more precision, the answers would be closer.

Source:
http://www.1728.org/polygon.htm