A painter measures a wall and determines it is 4.2 m by 3.3 m. high. The room is square and has a door that is 2 m x 1 m and two windows that are each 1.5 m x 1.5 m. How many yd2 of wall space needs to be painted? (1 m = 1.1yd)



Answer :

The room is square, it means it has 4 walls with same dimentions. Let's calculate the area of one of them.

[tex]A_w=4.2\times3.3=13.86m^{2}[/tex]

The total area is:

[tex]A_{4w}=4\times13.86=55.44m^{2}[/tex]

If we calculate now the area of each window and of the door, we just need to subtract these values from the total of the 4 walls to find the area that needs to be painted.

[tex]\begin{gathered} A_d=2\times1=2m^{2} \\ A_{win}=1.5\times1.5=2.25m^2\to A_{2win}=4.5m^{2} \end{gathered}[/tex]

The area to be painted is:

[tex]A_p=A_w-A_{2win}-A_d=55.44-2-4.5=48.94m^{2}[/tex]

To change it from m² to yd², we need to multiply it to 1.21, it is:

[tex]A_p=48.94\times1.21=59.2174yd^{2}[/tex]

The answer is: 59.23yd²