Question

Quadrilateral WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.

An isosceles trapezoid has sides of lengths 5,8,5 and 14. Find the length of the median.

Short answer

The length of the median is 11.

Step-by-step solution

Step 1. Check the figure.

Consider the figure representing the isosceles trapezoid.

Step 2. Step description.

Consider the trapezoid $ABCD$.

Here $\overline{XY}$is the median of the trapezoid $ABCD$.

Then the length of the median $\overline{XY}$is equal to the average of the base lengths $\overline{AB}$and $\overline{CD}$.

Step 3. Step description.

Find the length of the median as follows:

$\begin{array}{l}XY=\frac{1}{2}\left(AB+CD\right)\\ XY=\frac{1}{2}\left(8+14\right)\\ XY=\frac{22}{2}\\ XY=11\end{array}$

Therefore, the length of the median of the given trapezoid is 11.