The area will be, the area of the semi circle plus the area of the rectangle:
For the rectangle:
[tex]\begin{gathered} Ar=l\cdot w \\ Ar=10\cdot4=40in^2 \end{gathered}[/tex]For the semicircle:
[tex]\begin{gathered} As=\frac{\pi r^2_{}}{2} \\ As=\frac{25\pi}{2} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} A=Ar+As \\ A=40+\frac{25\pi}{2} \\ A\approx79.27in^2 \end{gathered}[/tex]