https://file.aiquickdraw.com/mathbot/file/1729087240848b60dmg5a.jpg

The figure shown in the image is a trapezoid, and we are asked to find its area. The formula to find the area of a trapezoid is given by:

\[
\text{Area} = \frac{1}{2} \times (a + b) \times h
\]

Where:
- \( a \) is the length of the top parallel side,
- \( b \) is the length of the bottom parallel side,
- \( h \) is the height of the trapezoid.

From the diagram, it's clear that the height \( h \) is equal to the value labeled as \( a \) (the vertical height), which is 7.7 inches. The base lengths are labeled as \( a \) and \( b \), where \( a = 7.7 \) inches (top) and \( b = 2.1 \) inches (bottom).

Now, applying the formula:

\[
\text{Area} = \frac{1}{2} \times (7.7 + 2.1) \times 7.7
\]
\[
\text{Area} = \frac{1}{2} \times 9.8 \times 7.7
\]
\[
\text{Area} = \frac{1}{2} \times 75.46
\]
\[
\text{Area} = 37.73 \, \text{square inches}
\]

Thus, the area of the trapezoid is **37.73 square inches**.

Would you like more details or have any questions?

Here are five related questions you might consider:
1. What would the area be if the height was different but the side lengths were the same?
2. How would you calculate the perimeter of this trapezoid?
3. What if the trapezoid had one non-parallel side—how would that affect the formula?
4. How do we calculate the area of a triangle using a similar method?
5. Can this formula be applied to 3D shapes like trapezoidal prisms?

**Tip:** Always double-check the units when performing area calculations to avoid confusion.

Find the area of the trapezoid, given a = 7.7 in and b = 2.1 in.

Learn how to find the area of a trapezoid with a top length (a) of 7.7 inches, bottom length (b) of 2.1 inches, and height (h) of 7.7 inches using the formula Area = 1/2 * (a + b) * h. This problem is suitable for middle school students in Grades 6-8.

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