Question

I need the :

Answer 1

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