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The image shows a trapezoid with an area of \(115 \, \text{cm}^2\), and its two parallel sides have lengths of \(12.4 \, \text{cm}\) and \(7.6 \, \text{cm}\). The height \(x\) is unknown, and we need to find its value.

The formula for the area of a trapezoid is:

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

Where:
- \(\text{Area} = 115 \, \text{cm}^2\)
- \(\text{Base}_1 = 12.4 \, \text{cm}\)
- \(\text{Base}_2 = 7.6 \, \text{cm}\)
- \(\text{Height} = x \, \text{cm}\)

Substituting the known values into the formula:

\[
115 = \frac{1}{2} \times (12.4 + 7.6) \times x
\]

Simplifying:

\[
115 = \frac{1}{2} \times 20 \times x
\]

\[
115 = 10x
\]

Now, solve for \(x\):

\[
x = \frac{115}{10} = 11.5 \, \text{cm}
\]

So, the height \(x\) of the trapezoid is \(11.5 \, \text{cm}\).

Would you like further details or have any other questions?

Here are some related questions:
1. How do you calculate the perimeter of a trapezoid?
2. What are the properties of an isosceles trapezoid?
3. How does changing the height of a trapezoid affect its area?
4. Can you derive the formula for the area of a trapezoid from the area of triangles?
5. What are the real-life applications of trapezoid area calculations?

**Tip:** When dealing with area problems, ensure all measurements are in the same unit before applying formulas.

The image shows a trapezoid with an area of 115 cm². The lengths of the parallel sides are 12.4 cm and 7.6 cm. The height (x) is unknown. Find the height of the trapezoid.

Learn how to calculate the height of a trapezoid when given its area and the lengths of the parallel sides. This problem involves applying the trapezoid area formula and solving a simple algebraic equation. Suitable for students in Grades 7-9.

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