# How Do I Find The Base Of A Trapezoid?

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.

thanked the writer.
The equation for area of a trapezoid is a=1/2*h(b1+b2).  To find the measure of missing base, you will multiply 1/2 times h, then divide each side by that product.  That will cancel the 1/2*h on one side, leaving you with area over half the height equal to b1 + b2.  Then subtract b1 from each side, which will result in the following equation: (area / (1/2*h)) - b1 = b2.

To plug in numbers, let's say area = 28; height = 4; and b1 =8.  We need to find b2.  When we substitute in to the original equation, it looks like this:
28 = 1/2*(4)(8 + b2)   Substitution
28/2 = (8 + b2)   Divide both sides by 1/2 height
14 - 8 = b   Subtract b1 from both sides
6 = b2   Simplify
The measure of the missing base is 6.
thanked the writer.
This formula should help

A = 1/2 × h × (a + b)

A= area
h= height
a= length of top
b= length of bottom

ok well now you have given me enough to work with ( I didn't know the height)

this is how your problem looks
A=44.25
h=5.9
a=6.7
now just plug those numbers into the equation
44.25=1/2*5.9*(6.7+b)
88.5= 5.9*(6.7+b)    divide by 1/2
15= 6.7+b      divide by 5.9
b=8.3

I know that answer is different than what the book says but that is the correct answer for the numbers you gave.
thanked the writer.
Oddman commented
The answer book is wrong more often than you might like. Sometimes I think the answer book represents a test of your self-confidence and understanding.
Anonymous commented
Take the answer and divide it by 2 then divide it by the height . Then take that answer and subtract it by base 2 and you get the answer
Anonymous commented
The formula is 1/2 (b1+b2)h