Answer:
[tex]143.8\:\mathrm{ft^2}[/tex]
Step-by-step explanation:
The composite figure shown in the picture consists of a semi-circle and a trapezoid. We can even break this trapezoid into a rectangle and two triangles for even simpler calculations. We can find the total area of the figure by simply adding the total area of the shapes we will break the figure into:
Area of semi-circle (half the area of a circle): [tex]\frac{1}{2}\cdot 4.5^2\cdot \pi[/tex]
Area of trapezoid (average of bases multiplied by height): [tex]16\cdot 7[/tex]
Thus, the total area of the figure is:
[tex]\frac{1}{2}\cdot 4.5^2\cdot \pi+16\cdot 7=143.808625618\approx \boxed{143.8\:\mathrm{ft^2}}[/tex]
