Answer:
Apothem = a = 8mm
perimeter = 32√3
area of outside = 128√3mm²
area of inside =64πmm²
area of shaded = 20.6 mm²
Step-by-step explanation:
Step 1
Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side
Apothem = a = 8mm
Step 2
Perimeter = the sum of the lengths of all the sides
perimeter = 6(s)
here s is length of one side
s = 2a /√3
= 2(8) /√3
= 16√3 / 3
perimeter = 6(16√3 / 3)
= 32√3
Step 3
Area of the whole figure
area = 1/2 x perimeter x apothem
area = 1/2(32√3)(8)
= 128√3mm²
Area of circle
πr²
π(8)²
64πmm²
Step 4
Area of shaded figure = Area of whole - Area of circle
= 128√3 - 64π
= 20.6 mm²
