Consider that the are of the given hexagon is the sum of the area of six triangles.
First, calculate the value of α, the height of the triangle, by using the Pythagoras theorem:
α = √(4² - (4/2)²)
α = √(16 - 4)
α = √12
α = √(4x3)
α = 2√3
next, use the formula for the area of a triangle:
A = bα/2
A = (4)(2√3)/2
A = 4√3
FInally, the area of the hegaxon is six times the are of the triangle:
AH = 6A
AH = 6(4√3)
AH = 24√3