The dimension for the first room is
![=12ft\text{ by 12ft}](https://img.qammunity.org/2023/formulas/mathematics/college/2yqjuwqmklfjcw61yyqo728gmk6at48r36.png)
By conversion,
![1squareyard=0.111\text{ square f}eet](https://img.qammunity.org/2023/formulas/mathematics/college/1kntl4cblg4kjnmqiq4j1a3f2jntgsdpm2.png)
The area of the first room will be
![\begin{gathered} =l* b \\ =12ft*12ft \\ =144ft^2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/7025p3clebg0kpnzke86oznalcm8zn0rke.png)
The second room has a dimension of
![=10ft\text{ b}y\text{ 14ft}](https://img.qammunity.org/2023/formulas/mathematics/college/bnryk8rh6zqeyjdkzq6kqvnkoi9fdmti1l.png)
The area of the second room will be
![\begin{gathered} =l* b \\ =10ft*14ft \\ =140ft^2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/bv9773sc0lwnc4vnx73bdzguor1r2w5rwm.png)
The dimension of the third room is
![21ft\text{ by 20ft}](https://img.qammunity.org/2023/formulas/mathematics/college/j69jedmgoud4tf8tobsomm7pukby1xwqqg.png)
The area of the third room will be
![\begin{gathered} =l* b \\ =21ft*20ft \\ =420ft^2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/x1ujjhys0q6lz8mcgbutto0kt7hwena6u9.png)
The total area of the three rooms will be
![\begin{gathered} =144ft^2+140ft^2+420ft^2 \\ =704ft^2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/zs1h9fxbknzw8jf3mtyc7in5obamry3fif.png)
Recall that
![\begin{gathered} 1squareyard=0.111\text{ square f}eet \\ 1squareyard=(1)/(9)ft^2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/9jht0681oarqasch0u9cze6v7puc6f1du7.png)
The final answer to be converted to the squared yard would be divide by 9
![\begin{gathered} =(704)/(9)sq\text{ yd} \\ =78.222\text{ sq yd} \\ \approx\text{ to the nearest tenth= 78.2 sq yd} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/gb6pj3eovh7ua6lgp0yqv6isff0nzui6fd.png)
Hence,
The number of square yards of carpet to be ordered = 78.2 sq yd