Question

1. given that the length of the median of a trapezoid is 8cm and the length of its lower base is 11cm, the length of the upper base is ______ cm.
2. in the figure, in trapezoid abcd, $overline{ad}paralleloverline{bc}$, e and f are the mid - points of $overline{ab}$ and $overline{cd}$, respectively, and ef = 6. the value of ad + bc is ______.

a. 9
b. 10.5
c. 12
d. 15

Explanation:

Step1: Recall trapezoid - median formula

The formula for the length of the median \(m\) of a trapezoid is \(m=\frac{a + b}{2}\), where \(a\) is the upper - base and \(b\) is the lower - base.

Step2: Solve for the upper - base of the first trapezoid

Given \(m = 8\) cm and \(b=11\) cm. Substitute into the formula \(8=\frac{a + 11}{2}\). Cross - multiply: \(16=a + 11\). Then \(a=16 - 11=5\) cm.

Step3: Solve for \(AD + BC\) of the second trapezoid

Since \(EF\) is the median of trapezoid \(ABCD\) and \(EF = 6\), and the formula for the median \(EF=\frac{AD + BC}{2}\). Cross - multiply: \(AD + BC=2\times EF\). Substitute \(EF = 6\) into the equation, we get \(AD + BC = 12\).

Answer:

1. 5
2. C. 12