Answer:
The area of the hexagon is approximately 55.43 square feet
Explanation:
The given apothem of the hexagon, a = 4 ft.
The area of an hexagon given the apothem, 'a', is found as follows;
The area of an hexagon of side length, s, A = ((3·√3)/2)·s²
s = a·2·tan(180/n)
∴ A = ((3·√3)/2)·(a·2·tan(180/n))²
For an hexagon, n = 6
∴ A = ((3 × √3)/2) × (4 × 2 × tan(180/6))² ≈ 55.43
The area of the hexagon, A ≈ 55.43 ft.²