Question

the area of the trapezoid is 33 square miles.
what is the trapezoids height, h?
h = \square 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 $A=33$, $b_1=8$, $b_2=3$. Plug these into the formula:
$33 = \frac{1}{2}(8 + 3)h$

Step3: Simplify the parentheses

Calculate the sum inside the parentheses:
$33 = \frac{1}{2}(11)h$
$33 = 5.5h$

Step4: Solve for h

Divide both sides by 5.5 to isolate $h$:
$h = \frac{33}{5.5}$
$h = 6$

Answer:

$h = 6$ miles