# How to Find the Area of a Trapezoid Part 3

This the third part of a series on finding the area of a trapezoid here in PH Civil Service Review. In the first post, we discussed the derivation of the area of a trapezoid and give a worked example. In the second post, we discussed how to find the area given the base and the height as well as to find the height given the area and the base.

In this post, we are going to find the base, given the height and the area. We continue with the fourth example.

Example 4

A trapezoid has area 65 square centimeters, height 13 cm, and base of 4 cm. Find the other base.

Solution

In this example, we have $A = 65$, $h = 13$ and $a = 4$. We are looking for $b$

$A = \frac{1}{2}h(a + b)$

$65 = \frac{1}{2}(13)(4 + b)$

In equations with fractions, we always want to eliminate the fractions. In the equation above, we can do this by multiplying both sides of the equation by 2.  That is,

$2(65) = 2(\frac{1}{2})(13)(4 + b)$.

The product of 2 and 1/2 is 1, so,

$130 = 13(4 + b)$.

Next, we use distributive property on the right hand side. Recall: $a(b + c) = ab + ac$.

$130 = 13(4) + 13(b)$

$130 = 52 + 13b$.

We want to find b, so we subtract 52 from both sides giving us

$78 = 13b$.

Next, we divide both sides by 13

$6 = b$.

So, the other base is 6 centimeters which is our answer to the problem.

Example 5

The figure below is a trapezoid. Find the value of $a$.

Solution

$A = \frac{1}{2}h(a + b)$

$70 = \frac{1}{2}(7) (a + 9)$

We eliminate the fraction by multiplying both sides by 2 to get

$140 = 7(a + 9)$.

Note: It will be shorter if we divide both sides of equation by 7. You might want to try it.

Using the distributive property, we have

$140 = 7(a) + 7(9)$

$140 = 7a + 63$.

Subtracting 63 from both sides, we have

$77 = 7a$.

Dividing both sides by 7, we have

$11 = a$,

So, the other base of the trapezoid is 11 units.

In the next post, we are going to summarize what we have learned from the this series.