To solve this problem, we need to find $x$, the length of $EF$, which lies in the trapezoid $ABCD$, where $AB \parallel DC$. The sides $AE$ and $BF$ are perpendicular to the parallel sides $AB$ and $DC$. This trapezoid includes a midsegment $EF$.

The Midsegment Theorem for Trapezoids

The midsegment (or median) of a trapezoid is equal to the average of the lengths of the two parallel bases: $EF = \frac{AB + DC}{2}$

Step 1: Substitute the given values

From the diagram:

• $AB = 20$
• $DC = 16$

$EF = \frac{AB + DC}{2} = \frac{20 + 16}{2}$

Step 2: Simplify the equation

$EF = \frac{36}{2} = 18$

Thus, the length of $EF$ ($x$) is:

$x = 18$

Let me know if you have any questions or would like further explanations!

5 Related Questions:

1. What is the formula for the area of a trapezoid, and how could we apply it here?
2. How would you calculate the height of the trapezoid using other information in the diagram?
3. If $EF$ were extended to form a parallelogram, what would be the length of its diagonals?
4. How would the solution change if $AB = 24$ instead of $20$?
5. How do the lengths of $AE$ and $BF$ affect the properties of this trapezoid?

Tip:

Always check if the given sides are parallel when applying the midsegment theorem, as it only applies to trapezoids with parallel bases!