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Question 964200: How to calculate the relative amounts of colour needed for a diamond shape?
As part of our assignment we have to create our own design for a quilt and I choose to do a diamond, but I need to calculate the amount of colour I would need but I do not know how to do it.
The functions that I have used to create the outer diamond are:
y=x+15 (-15< x <0)
y=-x-15 (-15< x <0)
y=x-15 (0< x <15)
y=-x+15 (0< x <15)
These functions are for the inner diamond:
y=x+10 (-10< x <0)
y=x-10 (0< x <10)
y=-5/5x+10 (0< x <10)
y=-5/5x-10 (-10< x <0)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I would think that by
y=-5/5x+10 you mean  , or simply  ,
and that by
y=-5/5x-10 you mean  , or simply  .
Those equations make a design like this:
 showing nested diamonds (or really nested squares).
If calculating areas was necessary, we know that the area of a rhombus is half the product of the diagonal lengths.
So, the area of the large square is  square units,
and the area of the smaller square is  square units.
We could invoke a lot of higher math, but not even the calculation of areas above is necessary to find the ratio of the areas.
I appreciate your effort at using math to describe the design.
without that (or a picture) I would have no idea of what your design was.
The description was complicated, but the calculation is very simple,
as in fifth grade math.
The smaller, inside square's diagonals are  as long as
the larger, outside square's diagonals.
The inside square is a scaled-down version of the outside one.
Its inside square's sides are the length of the outside square's sides,
and as a consequence, the inside square's area is
 the area of the outside square.
If you are going to cut squares in two sizes and sew one on top of another,
for every 9 feet of material for the larger square you will need 4 feet of material for the smaller square.
If, however, you are going to saw 4 trapezoids of the outside color,
forming a frame around the inside square,
that frame will be  of the area of the large outside square,
and since the smaller inside square has  of the area of the large outside square,
so the ratio of visible material areas is  in favor of the outside color.
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