Question

1. given trapezoid abcd, what is ef?

(image of trapezoid abcd with bc=24, ad=32, e on ab (with ae=eb), f on cd (with cf=fd), and ef connecting e and f)

Explanation:

Step1: Identify the midline property

In a trapezoid, the segment connecting the midpoints of the non - parallel sides (the midline or median) has a length equal to the average of the lengths of the two parallel sides. Here, \(E\) and \(F\) are midpoints of \(AB\) and \(CD\) respectively, so \(EF\) is the midline of trapezoid \(ABCD\).

Step2: Apply the midline formula

The formula for the length of the midline \(m\) of a trapezoid with parallel sides of lengths \(a\) and \(b\) is \(m=\frac{a + b}{2}\). Here, \(a = 24\) (length of \(BC\)) and \(b=32\) (length of \(AD\)). So we calculate \(EF=\frac{24 + 32}{2}\).
First, add the two lengths: \(24+32 = 56\). Then divide by 2: \(\frac{56}{2}=28\).

Answer:

28