To find the height of the trapezoid, we can use the formula for the area of a trapezoid:

$\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h$

where:

• $b_1 = 3$ meters (one base of the trapezoid)
• $b_2 = 7$ meters (the other base of the trapezoid)
• $\text{Area} = 25$ square meters
• $h$ is the height of the trapezoid (what we need to find)

Plugging in the known values:

$25 = \frac{1}{2} \times (3 + 7) \times h$

Simplify the equation:

$25 = \frac{1}{2} \times 10 \times h$

$25 = 5h$

Now solve for $h$:

$h = \frac{25}{5} = 5$

So, the height of the trapezoid is 5 meters.

Do you want more details or have any questions?

Here are 5 related questions to explore further:

1. How would the formula change if the trapezoid had different units of measurement?
2. How do you calculate the height if only the side lengths are given but not the area?
3. What are other properties of trapezoids that are useful in geometry?
4. How does the concept of a trapezoid's height apply to real-world problems?
5. How do you derive the area formula for a trapezoid from basic geometric principles?

Tip: Remember that knowing the formulas and when to apply them is key to solving many geometry problems efficiently.