Question

The garden is made up of a rectangular patch of grass and two semi-circular vegetable patches. If the dimensions of the rectangular patch are 16 m (length) and 8 m (width) respectively, calculate: a) the perimeter of the garden.
b) the total area of the garden.

Answer 1

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:
\(\displaystyle{A}={l}{w}+{2}{\left(\frac{{1}}{{2}}\right)}π{r}^{{2}}\)
\(\displaystyle{A}={\left({16}\right)}{\left({8}\right)}+{2}{\left(\frac{{1}}{{2}}\right)}π{\left({4}\right)}^{{2}}\)
\(\displaystyle{A}={128}+{16}π\sim{178.3}{m}^{{2}}\)