Question 1114436: A stop sigh is a regular octagon. The manufacturer can make 6 stop signs from a peice of 60 In by 90 in sheet metal. How much aluminum is left?
I already tried to find the area of 1 octagon by using the side length of 15 (even though one is not given) to find the perimeter and apothem, and put them in the area of a regular polygon formula, then multiplied the area I got by 6 and subtracted that number from the area of the aluminum, but I always got negative numbers because I ended up with the equation 5,400-6,518.4=-1,118.4 but since you can’t have a negative area, I know I’m doing it wrong.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A stop sigh is a regular octagon. The manufacturer can make 6 stop signs from a peice of 60 In by 90 in sheet metal. How much aluminum is left?
I already tried to find the area of 1 octagon by using the side length of 15 (even though one is not given) to find the perimeter and apothem, and put them in the area of a regular polygon formula, then multiplied the area I got by 6 and subtracted that number from the area of the aluminum, but I always got negative numbers because I ended up with the equation 5,400-6,518.4=-1,118.4 but since you can’t have a negative area, I know I’m doing it wrong.
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Obviously, the sides have to be less than 15 inches.
Even taking that into account, "stacking and packing" problems are not simple.
Octagons don't "mesh" like hexagons do, either.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! You have to know the correct length of a side of the octagon.
If it is not given. You can only guess. You did; that is why
you got an unacceptable result.
Cheers,
Stan H.
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