To find the area of the trapezoid, 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 \(\text{Base}_1\) and \(\text{Base}_2\) are the lengths of the parallel sides, and \(\text{Height}\) is the perpendicular distance between them.

From the given dataTo find the area of the trapezoid, 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 \(\text{Base}_1\) and \(\text{Base}_2\) are the lengths of the parallel sides, and \(\text{Height}\) is the perpendicular distance between them.

From the given 
- \(\text{Base}_1 = AB = 210\) units
- \(\text{Base}_2 = DE = 65\) units
- \(\text{Height} = 117.09\) units (calculated previously)

Now we can plug these values into the area formula:

\[
\text{Area} = \frac{1}{2} \times (210 + 65) \times 117.09
\]

First, calculate the sum of the bases:

\[
210 + 65 = 275
\]

Then, multiply by the height:

\[
275 \times 117.09 \approx 32199.75
\]

Finally, take half of this product to find the area:

\[
\frac{1}{2} \times 32199.75 \approx 16099.88
\]

So, the area of the trapezoid is approximately \(16099.88\) square units.

Would you like any further details or have any questions?

Here are 5 questions you can ask:
1. Can you explain how to derive the area formula for a trapezoid?
2. How can you find the area of a trapezoid if only the lengths of the diagonals and angles are known?
3. What are some real-world applications of calculating the area of trapezoids?
4. How do you calculate the perimeter of a trapezoid?
5. Can you explain how the trigonometric functions are used to find the height in this problem?

**Tip:** When calculating the area of complex shapes, breaking them down into simpler shapes (like triangles and rectangles) can often make the problem more manageable.

Learn how to calculate the area of a trapezoid using the formula Area = 1/2 * (Base1 + Base2) * Height. Follow a detailed step-by-step solution with given bases and height values. Suitable for Grades 7-9 students learning about geometric shapes and area calculations.

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