The surface area is the total area occupied by the object. The surface area of the painted figure is [tex]440m^2.[/tex]
From the attached box, we have the following:
[tex]L = 20m[/tex] -- length
[tex]W = 10m[/tex] --- width
[tex]H = \frac 45 \times 5m = 4m[/tex] --- the painted height
Since the box has an open-top, the surface area is:
[tex]Area = LW + 2(WH + LH)[/tex]
So, we have:
[tex]Area = 20 \times 10 + 2 \times (10 \times 4 + 20 \times 4)[/tex]
[tex]Area = 200 + 2 \times (120)[/tex]
[tex]Area = 200 + 240[/tex]
[tex]Area = 440[/tex]
Hence, the painted area is [tex]440m^2.[/tex]
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