Area of shaded region is 463 square units.
What is area of octagon?
Area of octagon = \(\frac{1}{2}\) × \(8\) × base × height
What is apothem of octagon?
The apothem of any polygon is equal to the line that connects the center of the polygon with one of its sides perpendicularly. Using the apothem, we can calculate the area of the polygons in an easier way.
Given
Apothem of the octagon = 13.28 units
Base of octagon = 11 units
Area of octagon = \(\frac{1}{2}\) × \(8\) × base × height
= \(\frac{1}{2}\) × \(11\) × \(13.28\) × \(8\)
= 584.32
Area of square = side × side
= 11 × 11
= 121
Area of shaded region = Area of octagon - Area of square
= 84.32 - 121
= 463.32
≅ 463 square units.
Hence, area of shaded region is 463 square units.
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