Question

unit 9 quadrilaterals mastery check #1
t r
12
x y
p a
40
xy =

Explanation:

Step1: Identify the trapezoid property

In a trapezoid, if a line segment connects the midpoints of the non - parallel sides (the legs), then its length is the average of the lengths of the two bases. Here, \(TR = 12\) (the top base) and \(PA=40\) (the bottom base), and \(XY\) connects the midpoints of the legs (since \(X\) is on \(TP\) and \(Y\) is on \(RA\), assuming it's the midline).

Step2: Apply the midline formula

The formula for the length of the midline \(m\) of a trapezoid is \(m=\frac{b_1 + b_2}{2}\), where \(b_1\) and \(b_2\) are the lengths of the two bases. Substituting \(b_1 = 12\) and \(b_2=40\) into the formula, we get \(XY=\frac{12 + 40}{2}\).

Step3: Calculate the value

First, add the two bases: \(12+40 = 52\). Then divide by 2: \(\frac{52}{2}=26\).

Answer:

26