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To solve for \( x \), we will use the given information in the diagram. Here's the approach:

- The area \( A \) of the trapezoidal shape is already given as \( 1620 \, \text{cm}^2 \).
- The trapezoid has two bases: the top (shorter) base is \( 9 \, \text{cm} \) and the bottom (longer) base is \( 41 \, \text{cm} \). The height of the trapezoid is \( x \).
  
The formula for the area of a trapezoid is:

\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]

Where:
- \( A = 1620 \, \text{cm}^2 \)
- \( b_1 = 9 \, \text{cm} \)
- \( b_2 = 41 \, \text{cm} \)
- \( h = x \)

Now, let's plug in the values and solve for \( x \):

\[
1620 = \frac{1}{2} \times (9 + 41) \times x
\]

\[
1620 = \frac{1}{2} \times 50 \times x
\]

\[
1620 = 25x
\]

\[
x = \frac{1620}{25}
\]

Now I'll calculate \( x \).

Calculate x from the trapezoidal area and given dimensions.

Solve for x in a trapezoid where the area is 1620 cm², the bases are 9 cm and 41 cm, and the height is unknown. This problem involves the formula for the area of a trapezoid and basic algebra. Suitable for students in Grades 7-9.

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