Question 184498
Surface Area of a Rectangular Box = (Area of Bottom Face + Area of Top Face ) + (Area of Right Face + Area of Left Face ) + (Area of Front Face + Area of Back Face)



This simplifies to:



Surface Area of a Rectangular Box = 2 * (Area of Top Face) + 2*(Area of Side Face) + 2*(Area of Front Face)



Note: Area of Bottom Face = Area of Top Face, Area of Right Face = Area of Left Face, and Area of Front Face = Area of Back Face



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Now let's draw a picture



<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/rectangularbox2.png">



From the drawing, we see that the front face (in red) is 12 inches wide and 6 inches high. So the area of the front face is 12*6=72 square inches.



Also, we see that the side face (in blue) is 15 inches long and 6 inches high. So the area of the side face is 15*6=90 square inches.



Finally, we see that the top face (in green) is 15 inches long and 12 inches wide. So the area of the top face is 15*12=180 square inches.



So the total surface area is:


Surface Area of a Rectangular Box = 2 * (Area of Top Face) + 2*(Area of Side Face) + 2*(Area of Front Face)



Plug in the areas we previously found:


Surface Area of a Rectangular Box = 2 * (180) + 2*(90) + 2*(72)



Multiply:


Surface Area of a Rectangular Box = 360 + 180 + 144



Add


Surface Area of a Rectangular Box = 684



So the total surface area of the rectangular box is 684 square inches