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.