Trapezoid ABCD, where AB is 8 and CD is 30。 Right angles on Angle BAD and Angle CDA。 Length of AD is 12。Solve for Area of ABCD

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.

Discover how to calculate the area of trapezoid ABCD, where AB = 8 cm, CD = 30 cm, and AD = 12 cm. This problem involves using the area formula for trapezoids and understanding the properties of right angles in geometry. Suitable for students in Grades 6-8.

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