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.

Performing transformations
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.

2020-10-19
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:
$$\displaystyle{A}={l}{w}+{2}{\left(\frac{{1}}{{2}}\right)}π{r}^{{2}}$$
$$\displaystyle{A}={\left({16}\right)}{\left({8}\right)}+{2}{\left(\frac{{1}}{{2}}\right)}π{\left({4}\right)}^{{2}}$$
$$\displaystyle{A}={128}+{16}π\sim{178.3}{m}^{{2}}$$