Question

Line XY is the mid-segment of trapezoid ABCD find the length of line XY

Answer 1

Length of line XY is 12cm

Explanation:

We apply the mid-segment of trapezoid theorem:

$\begin{gathered} \text{mid segment = }\frac{small\text{ base + big base}}{2} \\ \text{small base = AB} \\ \text{big base = DC} \end{gathered}$$\begin{gathered} \text{mid segment = }\frac{AB\text{ + DC}}{2} \\ AB\text{ = 9cm} \\ DC\text{ = 15cm} \\ \text{mid segment = }\frac{9\text{ + 15}}{2} \end{gathered}$$\begin{gathered} \text{midsegment = }\frac{24}{2} \\ \text{midsegment = }12 \\ XY\text{ = midsegment = 12cm} \end{gathered}$

Length of line XY is 12cm