Answer:
166 mm²
Explanation:
The area is given by ...
A = (1/2)Pa . . . . . where P is the perimeter and "a" is the apothem
One side of a 6-sided figure is shown as 8 mm, so the perimeter is ...
P = 6·(8 mm) = 48 mm
Filling in the apothem value, we have ...
A = (1/2)(48 mm)(4√3 mm) = 96√3 mm² ≈ 166 mm²
The area of the hexagon is about 166 mm².