Answer
(a) $P = (12+6~\pi)~in$
(b) $A = (18~\pi)~in^2$
Work Step by Step
(a) Since the radius is $6~in$, the diameter is $12~in$
We can find the length $L$ of half the circumference:
$L = \frac{1}{2}~\pi~d$
$L = \frac{1}{2}~\pi~(12~in)$
$L = (6~\pi)~in$
We can find the total perimeter of the region:
$P = (12+6~\pi)~in$
(b) We can find the area of half of the full circle:
$A = \frac{1}{2}~\pi~r^2$
$A = \frac{1}{2}~\pi~(6~in)^2$
$A = (18~\pi)~in^2$
