Wow ! We might actually have to do some work for this one.
First, you have to find the area of the rectangle. I guess, just now,
that means the one who has to do that is me.
We know that it's a rectangle, because they told us so.
The corners are located at
(1, 4)
(4, 7)
(8, 3)
and
(5, 0).
Do you remember how to find the distance between 2 points ?
Distance = √ (difference-in-'x' ² + difference-in-'y' ²)
The distance between the first 2 points is √(3² + 3²) = √18
The distance between point-2 and point-3 is √(4² + 4²) = √32
The distance between point-3 and point-4 is √(3² + 3²) = √18
The distance between point-4 and point-1 is √(4² + 4²) = √32 .
Notice that it wasn't really necessary to find all four distances.
As soon as I found the first two distances, I knew that one is the length
of the rectangle and the other one is the width of the rectangle, so I didn't
have to bother finding the other two, because I knew that they would be
the same as the first two. I just did it anyway, to make SURE that they
were the same. That helped me be sure that I didn't make any mistakes.
So here we are, outstanding in our field. (Actually, in Ms. Stone's field.)
We have a rectangle with a length of √32 units and a width of √18 units.
The area of any rectangle is (length) · (width)
= (√32 units) · (√18 units)
= √(32 · 18) units²
= √ (576) units²
= 24 units² .
We also know that each square unit on the map indicates 16 acres.
So the actual area of the field is
(24 units²) · (16 acres/unit²) = 384 acres .
Ms. Stone sold the field for $858,240 .
The unit sale price was
($858,240) / (384 acres) = $2,235 / acre .
Ms. Stone can now move into the city and live the life of a rich lady.
