# 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.