Answer:
46.20 square units
Step-by-step explanation:
The area of a regular polygon can be found from the side length and apothem as ...
A = (1/2)ap . . . . . where a = apothem, p = perimeter (# of sides times side length)
The total area of the pentagon is then ...
A = (1/2)(5.51)(5·8) = 110.20 . . . . . square units
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The shaded area is the difference between the area of the pentagon and the area of a square with side length 8. The square's area is ...
A = s^2 = 8^2 = 64 . . . . . . square units
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Then the shaded area is ...
A = (pentagon area) - (square area) = 110.20 -64.00 = 46.20 . . . . . square units
