Area: Pentagon with a circular hole

Geometry Level 4

The image above consists of an isosceles triangle,\(\triangle ABC\) where the height: \(h = 4 \text{ units}\); \(\overline{AB}=\overline{BC}\); and \(\angle ABC = 120^{\circ}\). \(\triangle ABC\) lies on top of the square \(ACDE\) and a circle of radius \(r\) is inscribed in the square \(ACDE\). Determine the area of the pentagon formed from combining the triangle \(ABC\) and the square \(ACDE\) minus the area of the inscribed circle.

Give your answer to one decimal place.

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