# How Do I Find Unknown Base Or Height Of The Trapezoid?

Understanding a trapezoid and how to find the area takes some basic background in math but is not so complex that it is out of reach of any logically thinking individual.  First you will need to write out the equation to find the area of a trapezoid: Area=height(b1+b2) / (2), you can then re-arrange the equation to determine the unknown base or height.

To find the measure of missing base, you multiply 1/2 times height, and then divide each side by that product.  Canceling the 1/2*h on one side, leaving you with area over half the height equal to b1 + b2.  You then subtract b1 from each side, which results in the following equation:  (area / (1/2*h)) - b1 = b2.

As an example set of numbers, let's say area = 36; height = 4; and b1 =8.  We need to find b2.

When we substitute in to the original equation, it looks like this:

Substitution: 36 = 1/2*(4) (8 + b2)
Divide both sides by 1/2 height: 36/2 = (8 + b2)
Subtract b1 from both sides: 18 - 8 = b2
Simplify: 10 = b2

The measure of the missing base in this example is 10.

When properly re-arranging the equation to solve for the missing height the equation becomes: Height= 2Area/(b1+b2).

When we substitute in to the original equation, it looks like this:

If the area is 30 and b1 is 4 and b2 is 6, then the equation can be written as "Height = 2 x 30/(4+6). Multiply 2 by 30 and you get 60. Add 4 and 6 to get 10. Divide 60 by 10 to solve for the height. In this example, the measure of the missing height is 5.

Take a few minutes and put these on paper, see how you do at solving a few examples.  Once you get the hang of the equations it’s not as hard as it appears.
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You work through the relevant relationships based on what you do know.
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Often such a problem gives information about the length of the bases, or the sides, and/or the area.

If you are given area and base lengths,
area = height*(base1 + base2)/2

So
height = 2*area/(base1 + base2)
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If you are given the lengths of the 4 sides, the problem is a little more complicated. You can work it by making use of the Pythagorean theorem, writing and solving 3 equations in 3 unknowns.
Let h be the height, b1 be the long base, s1 and s2 be the lengths of the sides, and b2 be the short base. We introduce auxiliary variables x and y. The three equations are
x2 + h2 = s12
y2 + h2 = s22
x + y + b2 = b1

Solving these gives
h = (√(-b1^4 + 4 b1^3 b2 - b2^4 + 4 b1 b2 (b2^2 - s1^2 - s2^2) - (s1^2 - s2^2)^2 + 2 b2^2 (s1^2 + s2^2) + 2 b1^2 (-3 b2^2 + s1^2 + s2^2)))/(2(b1 - b2))
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Ok, I don't an answer. But, I have a question for the last answer. I don't have the area since I need the height to find it !!!
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The height I know but the base I don't...

A= Area
B1= Base1
B2= Base 2   Now to calculate the height the formula is..
/= Divide

ax2/(Sum of B1 and B2)
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In short,

H=2(area/(b1+b2)
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The base1 of a trapezoid in which A=161.5cm squared, h=17cm, and b2=13cm
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B1 = [(A - B2) x 2] / 2
B2 = [(A - B1) x 2] / 2
H = (A x 2) / (B1 + B2)
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There are always two base of a trapezoid. You can find the bases by examining the figure. Two out of four sides of a trapezoid are parallel to each other. They are called the bases of the trapezoid. Now to find the height of the trapezoid, extend both the bases, so that you reach a point where they both end aright in front of each other. Join those two points and you will get the height of the trapezoid. If you want to read more details about it, you can visit the following link.
planetmath.org
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A=1/2h(b1+b2)
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