Question

what is the missing length?
5.6 km
u
18.6 km
area = 217.8 km²
u = \boxed{} kilometers

Explanation:

Step1: Recall the trapezoid area formula

The area \( A \) of a trapezoid is given by \( A=\frac{(a + b)}{2}\times h \), where \( a \) and \( b \) are the lengths of the two parallel sides, and \( h \) is the height (the perpendicular distance between them). Here, \( a = 5.6\) km, \( b = 18.6\) km, \( A = 217.8\) \( \text{km}^2 \), and \( h=u \). So we have the equation \( 217.8=\frac{(5.6 + 18.6)}{2}\times u \).

Step2: Simplify the sum of the parallel sides

First, calculate \( 5.6+18.6 = 24.2 \). The equation becomes \( 217.8=\frac{24.2}{2}\times u \).

Step3: Simplify the fraction

\( \frac{24.2}{2}=12.1 \), so the equation is \( 217.8 = 12.1\times u \).

Step4: Solve for \( u \)

To find \( u \), divide both sides of the equation by \( 12.1 \). So \( u=\frac{217.8}{12.1} \).

Step5: Perform the division

\( \frac{217.8}{12.1}=18 \).

Answer:

18