A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. What is the maximum area of a Norman window whose perimeter is $10$ feet?

$($For a diagram related to this problem refer to the pdf document in course content labeled: Calculus I Final Exam diagrams$).$

$($A$)\frac{32}{(4+)},$ sq$.$ ft

$\frac{128}{(4+)},$ sq$.$ft

$\frac{18}{(4+)},$ sq$.$ ft

$($D$)\frac{98}{(4+)},$ sq$.$ ft

$($E$)\frac{50}{(4+)},$ sq$.$ ft

$($F$)\frac{81}{(8+2)},$ sq$.$ft

$($G$)\frac{8}{(4+)},$ sq$.$ ft

$($H$)\frac{121}{(8+2)}$ sq$.$ ft

$(1)\frac{72}{(4+)}$ sq$.$ ft