To solve for $h$ using the formula $A = \frac{1}{2}h(b_1 + b_2)$, where:

• $A$ is the area of a trapezoid,
• $h$ is the height,
• $b_1$ and $b_2$ are the lengths of the parallel sides (bases).

We are given:

• $A = 44$,
• $b_1 = 4$,
• $b_2 = 7$.

Let's substitute these values into the formula:

$44 = \frac{1}{2}h(4 + 7)$

Now solve for $h$:

$44 = \frac{1}{2}h(11)$

$44 = \frac{11}{2}h$

Multiply both sides by 2 to get rid of the fraction:

$88 = 11h$

Now divide by 11:

$h = \frac{88}{11} = 8$

Thus, the height $h$ is 8 units.

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Would you like a more detailed explanation or have any other questions?

Here are 5 related questions you can explore:

1. How do you calculate the area of a triangle using a similar formula?
2. How does the trapezoid area formula change when the bases are equal?
3. Can you find the perimeter of the trapezoid with given side lengths?
4. How does the area formula for trapezoids differ from that of parallelograms?
5. What are real-world applications of trapezoid area calculations?

Tip: Always check if the dimensions are in consistent units when solving geometric problems.