Question

the dining room is rectangular and measures 13 ft 7 in by 19 ft 11 in. find the area of the dining room floor rounded to the nearest square foot.

Answer 1

`\begin{gathered} \text{the area of a rectangular figure is given by} \\ A=b\mathrm{}h \\ \text{where b is the base and h the height. In this case, we have mixed units, then we must convert} \\ \text{feets to inches or viceversa.} \\ \text{If we choose convert fe}ets\text{ to inches, we know that} \\ 1\text{ f}eet\text{ = 12 in} \\ \text{hence, } \\ \frac{1\text{feet}}{12\text{ in}}=1 \\ \text{Therefore,} \\ 7in=7in\cdot1 \\ 7in=7in\cdot(\frac{1\text{feet}}{12\text{ in}}) \\ 7in=(7)/(12)\text{feet} \\ 7in=0.58333\text{ fe}ets \\ In\text{ the same maner, } \\ 11in=11in\cdot1 \\ 11in=11in\cdot(\frac{1\text{feet}}{12\text{ in}}) \\ 11in=(11)/(12)\text{ f}eet \\ 11in=0.91666\text{ fe}et \\ \text{Hence, the base measures} \\ 13feets7in=13+0.58333\text{ f}eets=13.5833\text{ f}eets \\ \text{and the height:} \\ 19\text{ ft 11in=19+0.91666 fe}et=19.91666\text{ fe}ets \\ \text{FINALLY, THE AREA IS } \\ A=b\mathrm{}h \\ A=(13.5833)(19.91666)\text{ fe}ets^2 \\ A=(13.5833)(19.91666)\text{ fe}ets^2 \\ A=270.53f\text{e}ets^2 \\ By\text{ rounding to the nearest square foot, one has} \\ A=271\text{fe}ets^2 \end{gathered}`