Question

What is the length, in whole meters, of the plastic edging that Amy needs to complete this project?

Answer 1

The curved path edges are in a form of two pairs of quadrants. One pair is shown below:

We can find the lengths of the inner and outer arcs using the radii of 4m and 6m respectively.

The formula to find the length of the arc of a quadrant is

$L=\frac{1}{2}\pi r$

Length of inner arc:

$\begin{gathered} l=\frac{1}{2}\times\pi\times4 \\ l=6.3m \end{gathered}$

Length of outer arc:

$\begin{gathered} L=\frac{1}{2}\times\pi\times6 \\ L=9.4m \end{gathered}$

Hence, the length of the pair of arcs is

$6.3+9.4=15.7m$

For the two pairs, we have the length to be

$\begin{gathered} 15.7\times2 \\ =31.4m \end{gathered}$

Hence, it will take approximately 32 meters of plastic edging to complete the project.