Answer:
[tex](3 \pi+12)\ mm[/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]6[/tex] mm
step 1
Find the perimeter of rectangle
the perimeter of rectangle is equal to
[tex]P=2(b+h)[/tex]
we have
[tex]b=6\ mm[/tex]
[tex]h=3\ mm[/tex]
substitute
[tex]P=2(6+3)=18\ mm[/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=6\ mm[/tex]
substitute
[tex]C=\frac{1}{2}\pi (6)=3 \pi\ mm[/tex]
step 3
Find the perimeter of the figure
[tex]18\ mm+3 \pi\ mm-6\ mm=(3 \pi+12)\ mm[/tex]
