SOLUTION: A company wants to make cardboard boxes that are 15 inches long,12 inches wide, and 6 inches high. How many square inches of cardboard will the surface of the box have? I forgot

Question 184498: A company wants to make cardboard boxes that are 15 inches long,12 inches wide, and 6 inches high. How many square inches of cardboard will the surface of the box have? I forgot the formula. All i know is-
Surface area= 2(?*?)+2(?*?)+2(?*?)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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

------------------------------------------------------------

Now let's draw a picture

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

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