The figure described is a trapezoid $ABCD$ with the following characteristics:

• $AB = 8$ cm (the shorter parallel side)
• $CD = 30$ cm (the longer parallel side)
• $AD = 12$ cm (the height of the trapezoid)
• Angles $\angle BAD$ and $\angle CDA$ are right angles.

To find the area of trapezoid $ABCD$, we use the formula for the area of a trapezoid:

$\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$

Where:

• $\text{Base}_1 = AB = 8$ cm
• $\text{Base}_2 = CD = 30$ cm
• $\text{Height} = AD = 12$ cm

Step 1: Substitute the values into the area formula

$\text{Area} = \frac{1}{2} \times (8 + 30) \times 12$

$\text{Area} = \frac{1}{2} \times 38 \times 12$

$\text{Area} = 19 \times 12$

$\text{Area} = 228 \, \text{cm}^2$

Final Answer:

The area of trapezoid $ABCD$ is $228 \, \text{cm}^2$.

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Would you like any additional details or have other questions? Here are some related questions to consider:

1. How would you calculate the lengths of the non-parallel sides $BC$ and $DA$?
2. What would be the perimeter of the trapezoid $ABCD$?
3. How would the area change if $AB$ was extended to 12 cm?
4. How can you verify if trapezoid $ABCD$ is an isosceles trapezoid?
5. How does the area of trapezoid $ABCD$ compare with that of a rectangle with the same height and base lengths?

Tip: Always ensure that both bases and the height are perpendicular when calculating the area of a trapezoid.