Question

1. what is the length of \\( \overline { e f } \\)?

Explanation:

Step1: Identify the theorem

This is a trapezoid with a midline (or midsegment) \( \overline{EF} \). The midline of a trapezoid is the segment that connects the midpoints of the non - parallel sides, and its length is the average of the lengths of the two bases. The formula for the length of the midline \( m \) of a trapezoid with bases \( b_1 \) and \( b_2 \) is \( m=\frac{b_1 + b_2}{2} \). Here, \( b_1 = 22\) in (length of \( \overline{AB} \)) and \( b_2=27\) in (length of \( \overline{DC} \)).

Step2: Apply the formula

Substitute the values of \( b_1 \) and \( b_2 \) into the formula: \( EF=\frac{22 + 27}{2}\)
First, calculate the sum of the two bases: \( 22+27 = 49\)
Then, divide the sum by 2: \( \frac{49}{2}=24.5\)

Answer:

24.5 in