Question

what is the missing length?
6.4 mi
10 mi
z
area = 107 mi²

Explanation:

Step1: Recall trapezoid area formula

$A = \frac{1}{2}(b_1 + b_2)h$

Step2: Substitute known values

$107 = \frac{1}{2}(6.4 + z) \times 10$

Step3: Simplify the equation

$107 = 5(6.4 + z)$

Step4: Isolate the bracket term

$\frac{107}{5} = 6.4 + z$
$21.4 = 6.4 + z$

Step5: Solve for z

$z = 21.4 - 6.4$
$z = 14.6$

Answer:

14.6 mi