Question

A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is long and wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? (Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.)

Answer 1

Given: The image of the garden as shown

To Determine: The perimeter of the garden

Solution

Please note that the feet of fence required to build a fence round the garden is the perimeter of the garden

The perimeter of the garden would be the semi-circle plus two side length and a width

The perimeter of a semicircle can be calculated using the formula below

$\begin{gathered} Perimeter(semi-circle)=\frac{1}{2}\times2\pi r=\pi r \\ r=\frac{d}{2} \end{gathered}$

The diameter of the semi-circle is the same as the width of the rectangle. Therefore

$\begin{gathered} d=20ft \\ r=\frac{20ft}{2}=10ft \end{gathered}$$\begin{gathered} Perimeter(semi-circle)=\pi\times10 \\ =10\pi \\ =10\times3.14 \\ =31.4ft \end{gathered}$

The perimeter of the garden will be

$\begin{gathered} Perimeter(Garden)=28ft+20ft+28ft+31.4ft \\ =107.4ft \end{gathered}$

Hence, the feet of fence require to build a fence round the garden is 107.4 ft