If
the length of a rectangle is reduced by 3 meters and the
width is increased by 2 meters, the result is a square
whose area is the same as that of the rectangle. What
is that area?

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A
solution to this problem will appear along with
next month’s problem.

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May's
Problem

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The perimeter of a BIG
square is seven times the perimeter of a SMALL square.

What fraction of the area
of the BIG square is the area of the SMALL square?

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METHOD
1: Consider some examples. Construct the following chart. Let the perimeter
of the small square be convenient: 4, 8, 12, etc
and compute its sides and areas. Then compute
the perimeters, sides, and areas of the corresponding
BIG squares. Finally divide each pair of areas.
In each case the area of the SMALL square is
1/49 of the area of
the BIG square..
(Note: The wording of the question
indicates that the fraction is the same regardless
of the perimeter chosen for ont ot the squares.)

METHOD
2: Make a diagram.

SMALL
square
s=1 unit,
p = 4 units,
a = 1 square unit

BIG square
s = 7 units,
p = 28 units
(which is 7 times the perimeter of the SMALL square),
a = 49 square units.

So the area of the SMALL square is 1/49 the area
of the BIG square.

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April's
Problem

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The coordinates of the
vertices of quadrilateral ABCD are:

A(-4,-3), B(4,2), C(2,-2),
and D(6,-5).

What is the area of quadrilateral
ABCD?

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METHOD:
Break a larger figure into pieces. Sketch the diagram shown in the upper diagram.
Then, as shown in the lower
diagram, encase ABCD in a rectangle, partition the
newly formed excess region
into four triangles and a rectangle, and subtract
the total area of the five excess
regions from that of the rectangle. The area is
22.

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