a)The perimeter consists of the two lengths of the rectangle (16 m) and the two curve sides of the semicircles whose radius is half the width of the rectangle or \(\displaystyle\frac{{1}}{{2}}{\left({8}\right)}={4}\). Hence,

\(\displaystyle{P}={2}{l}+{2}{\left(\frac{{1}}{{2}}\right)}{\left({2}π{r}\right)}\)

\(\displaystyle{P}={2}{\left({16}\right)}+{2}{\left(\frac{{1}}{{2}}\right)}{\left({2}π\cdot{4}\right)}\)

\(\displaystyle{P}={32}+{8}π\sim{57.1}{m}\)

b)The total area is the area of the rectangle plus the areas of the semicircles:

\(\displaystyle{A}={l}{w}+{2}{\left(\frac{{1}}{{2}}\right)}π{r}^{{2}}\)

\(\displaystyle{A}={\left({16}\right)}{\left({8}\right)}+{2}{\left(\frac{{1}}{{2}}\right)}π{\left({4}\right)}^{{2}}\)

\(\displaystyle{A}={128}+{16}π\sim{178.3}{m}^{{2}}\)

\(\displaystyle{P}={2}{l}+{2}{\left(\frac{{1}}{{2}}\right)}{\left({2}π{r}\right)}\)

\(\displaystyle{P}={2}{\left({16}\right)}+{2}{\left(\frac{{1}}{{2}}\right)}{\left({2}π\cdot{4}\right)}\)

\(\displaystyle{P}={32}+{8}π\sim{57.1}{m}\)

b)The total area is the area of the rectangle plus the areas of the semicircles:

\(\displaystyle{A}={l}{w}+{2}{\left(\frac{{1}}{{2}}\right)}π{r}^{{2}}\)

\(\displaystyle{A}={\left({16}\right)}{\left({8}\right)}+{2}{\left(\frac{{1}}{{2}}\right)}π{\left({4}\right)}^{{2}}\)

\(\displaystyle{A}={128}+{16}π\sim{178.3}{m}^{{2}}\)