Question

what is the length of the the midsegment of a trapezoid with bases of length 16 and 24? the length of the midsegment of a trapezoid with the given bases is \boxed{}.

Explanation:

Step1: Recall the midsegment formula for a trapezoid

The formula for the length of the midsegment (or median) of a trapezoid is the average of the lengths of the two bases. The formula is \( m=\frac{b_1 + b_2}{2} \), where \( b_1 \) and \( b_2 \) are the lengths of the two bases.

Step2: Substitute the given values into the formula

Here, \( b_1 = 16 \) and \( b_2=24 \). Substituting these values into the formula, we get \( m=\frac{16 + 24}{2} \).

Step3: Simplify the expression

First, add the two bases: \( 16+24 = 40 \). Then divide by 2: \( \frac{40}{2}=20 \).

Answer:

20