The image shows a trapezoid labeled $ABCD$ with the following dimensions:

• $AB = 30$ units
• $CD = 10$ units
• The height of the trapezoid is 8 units.

We are tasked with finding the area of the trapezoid.

The formula for the area of a trapezoid is:

$A = \frac{1}{2} \times (b_1 + b_2) \times h$

Where:

• $b_1$ and $b_2$ are the lengths of the parallel sides (in this case, $AB$ and $CD$),
• $h$ is the height of the trapezoid.

Let me calculate that for you.

$A = \frac{1}{2} \times (30 + 10) \times 8$

Let me compute this.The area of the trapezoid is $160 \, \text{square units}$.

Let me know if you would like further clarification or more details.

Here are 5 related questions to extend this concept:

1. How would the area change if the height of the trapezoid doubled?
2. What is the perimeter of this trapezoid given the lengths of the non-parallel sides?
3. Can you calculate the area of a parallelogram with the same height and one of the trapezoid's base lengths?
4. How does the area of a trapezoid compare to that of a triangle with the same base and height?
5. What happens to the area of the trapezoid if one of the parallel sides shrinks to zero?

Tip: For geometric shapes, always keep the key formula handy—understanding how to manipulate it for different dimensions will make solving problems much easier.