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June's Problem
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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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For many additional problems we highly recommend the following books:

Math Olympiad Contest Problems for Elementary and Middle Schools by Dr. G. Lenchner
and
Math Olympiad Contest Problems Volume 2 edited by Richard Kalman
and
MOEMS® Contest Problems Volume 3
edited by Richard Kalman & Nicholas J. Restivo.
are sources of many such problems.

Creative Problem Solving in School Mathematics 2nd Edition by Dr. George Lenchner
can help you to teach solving these types of problems