# How to find the smaller basis of a trapeze

Is called the smaller basis of a trapeze (or the small basis) smaller of its parallel parties. Length of this party can be found in different ways, using various data. This article is also devoted to ways of its stay.

## It is required to you

• Lengths of the big basis, average line, trapeze height, area of a trapeze

## Instruction

1. It is the simplest to find the small basis, knowing the big basis of a trapeze and its average line. On property of a trapeze, its average line is equal to the half-sum of the bases. Then the small basis of a trapeze can be expressed as: b = 2m-a where m is the average line of a trapeze, an is the big basis of a trapeze.

2. If the area of a trapeze, its height and also length of the big basis is known, then it is enough to find the small basis. On a formula of the area of a trapeze of S = h(a+b)/2. Therefore, b = (2S/h) - a.

3. Let ABCD trapeze - acute-angled (as in the drawing). Then its small basis can be calculated through big, height and corners at the big basis (we will designate them for x and y). this case length of the small basis can be expressed through these data so: b = a-h * (ctg(x)+ctg(y)).

4. Let now this trapeze obtusangular (we will assume that y corner - stupid). In this case the small basis can be expressed so: b = a-h (ctg(x) - ctg(180-y)).

Author: «MirrorInfo» Dream Team