Answer
Total cost of resurfacing the path around the pool is\[\$600\].
Work Step by Step
Compute the area (A) of the outer rectangle ABCD as follows:
\[\begin{align}
& A=\left( EH+EA+HD \right)\left( AE+EF+FB \right) \\
& =\left( 14\text{ ft}+3\text{ ft+3}\,\text{ft} \right)\left( 30\text{ ft}+3\text{ ft+3}\,\text{ft} \right) \\
& \text{= 720 ft}{{.}^{2}}
\end{align}\]
Compute the area of the inner rectangle EFGH (swimming pool) as follows:
\[\begin{align}
& A=l\times b=EG\cdot EF \\
& =14\text{ ft}\times 30\text{ ft} \\
& \text{= 420 ft}{{.}^{2}}
\end{align}\]
So, the area of the path will be the difference between the two:
\[\begin{align}
& \text{Area of path}=720\text{ f}{{\text{t}}^{2}}-420\text{ f}{{\text{t}}^{2}} \\
& \text{= 300 f}{{\text{t}}^{2}}
\end{align}\]
The cost of resurfacing the path will be calculated by multiplying it by per square rate.
\[\begin{align}
& \text{Cost}=\$2\times300\text{f}{{\text{t}}^{2}}\\&=\text{}\!\!\$\!\!\text{600}\end{align}\]
Hence, total cost of resurfacing the path around the pool is\[\$600\].
