Question

bear is a trapezoid, with median ds. find the length of \\(\overline{ds}\\).

image of trapezoid bear with e at top-left, a at top-right, r at bottom-right, b at bottom-left. ea is 12, br is 16, d is on eb, s is on ar, ds is the median.

\\(\circ\\) \\(ds = 14\\)
\\(\circ\\) \\(ds = 18\\)
\\(\circ\\) \\(ds = 28\\)
\\(\circ\\) \\(ds = 15\\)

Explanation:

Step1: Recall trapezoid median formula

The median (or midline) of a trapezoid is the average of the lengths of the two parallel sides. The formula is \( DS=\frac{EA + BR}{2} \), where \( EA \) and \( BR \) are the lengths of the two bases.

Step2: Substitute the given values

We know \( EA = 12 \) and \( BR = 16 \). Substitute these into the formula: \( DS=\frac{12 + 16}{2} \).

Step3: Calculate the result

First, add the numerator: \( 12 + 16 = 28 \). Then divide by 2: \( \frac{28}{2}=14 \).

Answer:

DS = 14