Question

the area of the trapezoid is 48 square miles.
what is the trapezoids height, h?
h = \boxed{} miles

Explanation:

Step1: Recall trapezoid area formula

The area of a trapezoid is given by $A = \frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are the lengths of the two parallel sides, and $h$ is the height.

Step2: Substitute known values

We know $A=48$, $b_1=6$, $b_2=10$. Plug these into the formula:
$48 = \frac{1}{2}(6 + 10)h$

Step3: Simplify the parenthetical term

Calculate the sum inside the parentheses:
$48 = \frac{1}{2}(16)h$
$48 = 8h$

Step4: Solve for $h$

Divide both sides by 8 to isolate $h$:
$h = \frac{48}{8}$

Answer:

$h = 6$ miles