Question

The dimensions of a room with one window and one door at a community center shown. Ivan wants to have the four walls painted. The painter says the area is 542.2 square ft. Estimate the total area that needs to be painted. Was the painters answer reasonable?Explain

Answer 1

We need to calculate the surface area, the surface area of a prism is given by:

$\begin{gathered} SA=2(lw+lh+wh) \\ w=width=38\frac{3}{8}=\frac{307}{8}_{} \\ l=length=29\frac{1}{2}=\frac{59}{2} \\ h=height=8 \end{gathered}$

Therefore:

$\begin{gathered} SA=2(\frac{307}{8}\cdot\frac{59}{2}+\frac{59}{2}\cdot8+\frac{307}{8}\cdot8) \\ SA=3350.125ft^2 \end{gathered}$

If we remove the ceiling and the floor:

$\begin{gathered} SA=3350.125-2(\frac{307}{8}\cdot\frac{59}{2}) \\ SA=1086ft^2 \end{gathered}$

The painters answer wasn't reasonable at all, they said the area was 542.2ft², which is quite different from 1086ft²