Question

the area of the trapezoid is 42 square kilometers.
what is the trapezoids height, h?
h = \boxed{} kilometers

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 $A=42$, $b_1=4$, $b_2=8$. Substitute into the formula:
$42 = \frac{1}{2}(4 + 8)h$

Step3: Simplify the parenthetical term

Calculate the sum inside the parentheses:
$42 = \frac{1}{2}(12)h$
$42 = 6h$

Step4: Solve for $h$

Divide both sides by 6:
$h = \frac{42}{6}$

Answer:

$h = 7$ kilometers