Answer
The area of the tile required to cover the kitchen floor is\[148\text{ ft}{{\text{.}}^{\text{2}}}\].
Work Step by Step
The area of the tile needed to cover the kitchen floor will be calculated by subtracting the areas covered by the stove and the refrigerator, from the area of the kitchen floor.
Area of the kitchen floor will be:
\[\begin{align}
& {{A}_{1}}=12\text{ ft}\times 15\text{ ft} \\
& =180\text{ f}{{\text{t}}^{\text{2}}}
\end{align}\]
The area covered by the stove will be:
\[\begin{align}
& {{A}_{2}}=3\text{ ft}\times 4\text{ ft} \\
& =12\text{ ft}{{\text{.}}^{\text{2}}}
\end{align}\]
The area covered by the refrigerator will be:
\[\begin{align}
& {{A}_{3}}=4\text{ ft}\times 5\text{ ft} \\
& =\text{20 f}{{\text{t}}^{\text{2}}}
\end{align}\]
So, the area of the tile needed to cover the kitchen floor will be:
\[\begin{align}
& A={{A}_{1}}-\left( {{A}_{2}}+{{A}_{3}} \right) \\
& =180\text{ f}{{\text{t}}^{2}}-\left( 12\text{ f}{{\text{t}}^{2}}+20\text{ f}{{\text{t}}^{2}} \right) \\
& =\text{148 ft}{{\text{.}}^{\text{2}}}
\end{align}\]
Hence, the area of the tile needed in order to cover the kitchen floor is\[148\text{ ft}{{\text{.}}^{\text{2}}}\].
