The problem asks to find the length of the midsegment $MN$ of a trapezoid $ABCD$. The lengths of the two bases are given as $AB = 21$ and $DC = 37$.

1. Problem Description

The problem asks to find the length of the midsegment $MN$ of a trapezoid $ABCD$. The lengths of the two bases are given as $AB = 21$ and $DC = 37$.

2. Solution Steps

The midsegment of a trapezoid is a line segment connecting the midpoints of the non-parallel sides. The length of the midsegment is the average of the lengths of the two bases.

The formula for the length of the midsegment is given by:

$MN = \frac{AB + DC}{2}$

We are given that $AB = 21$ and $DC = 37$. Substituting these values into the formula, we have:

$MN = \frac{21 + 37}{2}$

$MN = \frac{58}{2}$

$MN = 29$

3. Final Answer

The length of the midsegment $MN$ is 29.