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Cutting a shape into two equal area shapes

Puzzling Asked by Moti on August 14, 2021

Given the following shape – an hexagon ABCDEF of which a parallelogram CDGH is cut out.
With a single cut divide the shape into two equal area shapes by means of an unmarked .

You may draw lines and points to find the cut. It is not too hard but interesting feature to exercise.

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2 Answers

Here is a conceptually very simple solution:

Answered by Paul Panzer on August 14, 2021

The question allows drawing of lines and points. In addition, the parallelogram is already cut out. If we draw the diagonal DH, the parallelogram is cut into two equal triangles, because in parallelograms the two opposite sides are always equal and both have the same third side DH. All vertices of a regular hexagon lie on the circumference. If we draw the straight line AD without doing any cutting, this line divides the hexagon into two equal areas because point D is opposite point A. We put the two triangles DHC and DHG as shown in the drawing. The areas of the two half hexagons which are not covered by the triangles are equal.

jan24

Answered by Vassilis Parassidis on August 14, 2021

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