Junaid has a rectangular box open from the top as in the figure. He paints base and 4 lateral faces as shown. He paints only up to th of the height of the box to save paint. Find the total surface area he painted.

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MrRoyal MrRoyal · Answer 1 · 2021-08-27T22:27:13+02:00

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]