Posted by **algebrajunkie** on Tuesday, April 26, 2011 at 8:40pm.

Shellie pays $4.00 for a square piece of wood, which she makes into a stop sign by cutting the corners off. what is the cost of the wasted part?

I don't even know where to begin?

do I take $4.00*1/8....which equals half and subtract that from 4.00...getting $2.50

- college algebra -
**drwls**, Tuesday, April 26, 2011 at 9:10pm
Check this out:

http://en.wikipedia.org/wiki/Stop_sign

It looks like 2/9 of the original square gets removed.

- college algebra -
**Reiny**, Tuesday, April 26, 2011 at 9:11pm
Each of the cut-off corners would be an isosceles right-angled triangle.

The stop sign will be an octagon with each side equal to x.

Consider one of the triangles, the hypotenuse will be x.

by Pythagoras you can show that each of the equal sides must be x/√2

each side of the original square is then equal to

x/√2 + x + x/√2 = x(2+√2)/2

and the original area = x^2(2+√2)^2/4 = x^2(3+2√2)/2

area of one triangle = (1/2)(x/√2)(x/√2) = x^2/4

or the total wasted part is x^2

so the part wasted is x^2/(x^2(3+2√2)/2))($4)

= 8/(3+2√2) dollars or appr. $1.37

- correction: college algebra -
**Reiny**, Tuesday, April 26, 2011 at 9:19pm
typo!

last part should be .....

each side of the original square is then equal to

x/√2 + x + x/√2 = x(2+√2)/√2

and the original area = x^2(2+√2)^2/2 = x^2(3+2√2)

area of one triangle = (1/2)(x/√2)(x/√2) = x^2/4

or the total wasted part is x^2

so the part wasted is x^2/(x^2(3+2√2))($4)

= 4/(3+2√2) dollars or appr. $0.69

- college algebra -
**drwls**, Tuesday, April 26, 2011 at 9:23pm
Reiny is correct for a regular octagon. In looking at the figure of

http://en.wikipedia.org/wiki/Stop_sign

I erroneously assumed that each pair of cut-off corners amounted to 1/9 of the square. That would amoount to $0.89 wasted.

## Answer this Question

## Related Questions

- algebra math - Lucas makes crosses out of a scrap piece of wood by cutting it ...
- calculus - right circular cylindrical tin cans are to be manufactured to ...
- calculus - A 33 by 33 square piece of cardboard is to be made into a box by ...
- algebra - Volume of a Box A box is constructed by cutting out square corners of ...
- college algebra word problem - An open box is made from a square piece of ...
- college algebra - An open box is made from a square piece of cardboard 20 inches...
- Mathematics - A regular octagon is formed by cutting off the corners of a square...
- Math--Please Help - A pizza bx with a square base is to be made from a ...
- Math - A man is cutting a board that is 6 3/4 ft into pieces that are 8 inches ...
- College Algebra - a box with an open top is constructed from a rectangular piece...