Median of a Trapezoid | Caddell Prep Online

Learn about the median of a trapezoid and its relationship to the two bases.

The median of a trapezoid is the average measurement of the two opposite parallel sides.

Here is an example:

The top side of the trapezoid is equal to $x + 5$ , the bottom base is equal to $3x + 1$ and the median is equal to 13, and is drawn between these two lines.

To find the median, just find the average length of the two lines, or vice versa.
Given the information, we can write out:
$13 = \frac{1}{2}((x + 5) + (3x + 1))$
And then solve for $x$ :
$13 = \frac{1}{2}(4x + 6)$
$13 = 2x + 3$
$10 = 2x$
$x = 5$

Now that we have x, we can plug it into the measurements of the other lines to solve for their lengths.
For the top side, we get:
$x + 5$
$(5) + 5$
$10$
And for the bottom side, we get:
$3x + 1$
$3(5) + 1$
$16$