If in a quadrangle only two opposite sides are parallel, it is possible to call it a trapeze. Couple of nonparallel pieces forming this geometrical figure are called sides, and other couple - the bases. The distance between two bases determines height of a trapeze and can be calculated in several ways.
Instruction
1. If in conditions lengths of both bases are given (with an and b) and the area (S) of a trapeze, begin calculation of height (h) with finding of the half-sum of lengths of the parallel parties: (a+b)/2. Then divide the square into the received value - result and will be required size: h = S/((a+b)/2) = 2*S / (a+b).
2. Knowing length of the average line (m) and the square (S) it is possible to simplify a formula from the previous step. By definition the average line of a trapeze is equal to the half-sum of its bases therefore for calculation of height (h) of a figure just divide the square at length of the average line: h = S/m.
3. It is possible to determine height (h) of such quadrangle and in case are given only length of one of sides (c) and the corner (α) formed by it and the long basis. In this case it is necessary to consider the triangle formed by this party, height and a short piece of the basis which is cut by height lowered on it. This triangle will be rectangular, the known party will be in it a hypotenuse, and height - a leg. The relation of lengths of a leg and a hypotenuse is equal to a sine opposite to a corner leg therefore for calculation of height of a trapeze increase the known length of the party by a sine of the known corner: h = с*sin(α).
4. The same triangle should be considered and if are given side length (c) and corner size (β) between it and other (short) basis. In this case corner size between side (hypotenuse) and height (leg) will be on 90 ° less than the corner, known from conditions: β-90 °. As the relation of lengths of a leg and a hypotenuse is equal to a cosine of the angle between them, calculate height of a trapeze multiplication of a cosine of the corner reduced by 90 ° by side length: h = c*cos (β-90 °).
5. If the circle of the known radius (r) is entered in a trapeze, the formula of calculation of height (h) will be very simple and will not demand knowledge of any other parameters. Such circle by definition has to concern each of the bases only one point and these points will lie on one line with the center of a circle. It means that the distance between them will be equal to diameter (the doubled radius) which is carried out perpendicular to the bases, that is coinciding with trapeze height: h=2*r.