In geometry, a quadrilateral with one pair of parallel sides is referred to as a trapezoid. There is also some disagreement on the allowed number of parallel sides in a trapezoid. The issue is whether parallelograms, which have two pairs of parallel sides, should be counted as trapezoids. Some authors define a trapezoid as a quadrilateral having exactly one pair of parallel sides, thereby excluding parallelograms. Other authors define a trapezoid as a quadrilateral with at least one pair of parallel sides, making the parallelogram a special type of trapezoid (along with the rhombus, the rectangle and the square). The latter definition is consistent with its uses in higher mathematics such as calculus. The former definition would make such concepts as the trapezoidal approximation to a definite integral is ill-defined.

To work out the base of a trapezoid you have to use the formula for working out the area, but obviously you will need to rearrange it so that you end up working out the base either (a) or (b) . The formula is as follows:

A = half (0.5) x h x ( a + b )

A and b are the lengths of the parallel sides, and h is the height the perpendicular distance between these sides. In 499 CE Aryabhata, a great mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy used this method in the Aryabhatiya. This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point.

A = area

h = height

a = length of top

b = length of bottom

Rearrange formula as follows:

A + b = A/(0.5 x h)

b = [A/(0.5 x h)] - a

Example :

A = 225

h = 15

a = 10

b = ?

225 = half (0.5) x 15 x ( 10 + b )

Rearrange

10 + b = 225/(0.5x15)

b = 30 - 10

b = 20

NEW FORMULA

A= Area

H= Height

B1= Unknown base number

B2= Known base number

b1= [A /(1/2 H)] - b2

b1 (unknown base number) equals [Area DIVIDED BY (one-half times Height)] minus b2 (known base

number).

Note

B1 and B2 are interchangeable.