Given that Jennifer is cutting a piece of fabric, where the top of the piece measures two feet, the bottom measures three feet, and each side measures four feet, determine the shape she is cutting the fabric.
In this piece of fabric, we’re told that the bottom of the fabric measures three feet and the top measures two feet. Each side of this, we’re told, measures four feet. The first thing we could say about this shape given it has a top, a bottom, and sides, is that it must be some sort of quadrilateral or four-sided shape. Let’s see if we can be more specific.
If we look at this given diagram, which is drawn to scale, in fact, the left side of this quadrilateral is only 3.75 feet. So, let’s see if we can shift the top across to make this four feet. Now, we can see that the side measures four feet. But what about the other side? Well, in fact, when we measure it, it only measures 3.5 feet. And we really need it to measure four feet. So, this diagram wouldn’t work.
Let’s see if we can try centering the base of this fabric directly below the top of the fabric. When we have this in a position where one side is four feet, then if the base of the fabric is centered directly below, then the other side should also be four feet. Now that we’ve found a piece of fabric that fits these dimensions, what can we say about its properties?
As we drew two horizontal lines for the top and the bottom of this fabric, we can say that these two lines would be parallel. The other two sides of this quadrilateral of four feet each are not parallel. So, we can say that this quadrilateral has one pair of parallel sides. And so, this piece of fabric must be in the shape of a trapezoid because the definition of a trapezoid is that it’s a quadrilateral with one pair of parallel sides.
If we wished, we could also note that the two nonparallel sides in this fabric are congruent, which means that it would be, an isosceles trapezoid. However, it’s sufficient to say that this piece of fabric is a trapezoid.