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Find the area of trapezoid cdef round your answer to the nearest tenth if necessary 

To find the area of trapezoid \( CDEF \), we use the area formula for a trapezoid:

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

In this trapezoid:
- \( \text{Base}_1 = 20.9 \, \text{in} \) (segment \( CD \)).
- \( \text{Base}_2 = 7.6 \, \text{in} \) (segment \( EF \)).
- \( \text{Height} = 11.4 \, \text{in} \) (the perpendicular distance from \( EF \) to \( CD \)).

Now, substituting these values into the formula:

\[
\text{Area} = \frac{1}{2} \times (20.9 \, \text{in} + 7.6 \, \text{in}) \times 11.4 \, \text{in}.
\]

First, calculate the sum of the bases:

\[
20.9 + 7.6 = 28.5 \, \text{in}.
\]

Next, calculate the area:

\[
\text{Area} = \frac{1}{2} \times 28.5 \, \text{in} \times 11.4 \, \text{in} = 162.45 \, \text{square inches}.
\]

Rounding to the nearest tenth:

\[
\text{Area} \approx 162.5 \, \text{square inches}.
\]

So, the area of trapezoid \( CDEF \) is \( \boxed{162.5} \) square inches.

Would you like more details or have any questions?

Here are five related questions to explore:
1. How would the area change if one of the bases increased?
2. How do you find the area of a trapezoid if only the side lengths and diagonals are known?
3. Can the height be determined from the other sides of the trapezoid using trigonometry?
4. How do you find the perimeter of trapezoid \( CDEF \)?
5. What would happen to the area if the trapezoid was reflected or rotated?

**Tip:** In any trapezoid, the height is always perpendicular to both bases, even if it’s not explicitly marked.

Learn how to find the area of trapezoid CDEF using the area formula for trapezoids. Follow a detailed step-by-step solution, including the values of Base 1, Base 2, and Height. Rounded to the nearest tenth, the area is 162.5 square inches. Suitable for students in Grades 6-8.

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