How to find the smaller base of the trapezoid

Smaller base of the trapezoid (or a small base) is the least of its parallel sides. The length of this side you can find a variety of ways, using a variety of data. That is the way they are being addressed in this article.

You will need

• The length of the major base, the midline, the height of a trapezoid, area of trapezoid

Instruction

1. The easiest way to find the small base, knowing the large base of the trapezoid and its mid. Property of a trapezoid, its middle line is equal to the sum of the bases. Then the small base of the trapezoid can be expressed as: b = 2m-a, where m is the middle line of a trapezoid, a large base of the trapezoid.
2. If you know the area of a trapezoid, the height and length of a large base, it is enough to find the small base. According to the formula area of a trapezoid S = h(a+b)/2. Therefore, b = (2S/h)-a.
3. Let the trapezoid ABCD is angled (as shown). Then its small base can be calculated through a large, elevation and angles with a large base (let's call them x and y).
   In this case, the length of the small base can be represented using this data is: b = a-h*(ctg(x)+ctg(y)).
4. Now let the notch-line (assume that the angle y is stupid). In this case, the small base can be expressed as: b = a-h(ctg(x)-ctg(180-y)).