Answer:
Option A [tex](4 \pi+26)\ in[/tex]
Step-by-step explanation:
we know that
The perimeter of the figure is equivalent to the perimeter of a rectangle plus the perimeter of semicircle minus the length side of [tex]8[/tex] inches
step 1
Find the perimeter of rectangle
the perimeter of rectangle is equal to
[tex]P=2(b+h)[/tex]
we have
[tex]b=8\ in[/tex]
[tex]h=9\ in[/tex]
substitute
[tex]P=2(8+9)=34\ in[/tex]
step 2
Find the circumference of semicircle
the of circumference of semicircle is equal to
[tex]C=\frac{1}{2}\pi D[/tex]
we have
[tex]D=8\ in[/tex]
substitute
[tex]C=\frac{1}{2}\pi (8)=4 \pi\ in[/tex]
step 3
Find the perimeter of the figure
[tex]34\ in+4 \pi\ in-8\ in=(4 \pi+26)\ in[/tex]
