The Mathematics Education Department
EMT 725, Lisa F. Garey

Folding to Obtain Equal Areas

Click here for the Problem statement

We want the yellow, blue, and green areas to be equal.

Observe that the trapezoids on the side are made up of a triangle and a rectangle. One half of the middle yellow triangle is equal to the triangle part of the trapezoid. Thus, the other half of the yellow triangle needs to be equal in area to the rectangle part of the trapezoid.

Area of triangle = Area of rectangle

1/2 *h*(b-a)=ah

b-a =2a

b = 3a

Thus, the height of the middle triangle is 2/3 of the long side of the trapezoid.

So, we know where the point should be, but creasing thirds is rather tricky. More algebra and geometry, I suppose.....

Consider making the crease extend to the short side of the paper. Then we have 2 similar triangles and we have the relationship

? = (1/4)a

Folding one-fourth is much more precise than folding one-third.

Here are the steps to folding the paper such that the yellow, blue, and green areas are equal.

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