Question

1. find mn

Explanation:

Step1: Identify the trapezoid midsegment rule

This figure is a trapezoid, and $MN$ is the midsegment (median) of trapezoid $ADGJ$. The formula for the midsegment of a trapezoid is $\text{Midsegment} = \frac{1}{2} \times (\text{sum of the two parallel bases})$.

Step2: Substitute the given values

The lengths of the parallel bases are $AD = 67$ and $JG = 30$. Substitute these into the formula:
$MN = \frac{1}{2} \times (67 + 30)$

Step3: Calculate the sum and product

First compute the sum inside the parentheses: $67 + 30 = 97$. Then multiply by $\frac{1}{2}$:
$MN = \frac{1}{2} \times 97 = 48.5$

Answer:

$48.5$