Here's a geometry problem where the solution equals 5000:

**Problem:**
Find the area of a trapezoid with bases \( a \) and \( b \), and height \( h \), if the area equals 5000 square units.

The formula for the area of a trapezoid is:
\[ \text{Area} = \frac{1}{2} (a + b) h \]

Given:
\[ \frac{1}{2} (a + b) h = 5000 \]

Let's assume:
\[ a = 100 \, \text{units} \]
\[ b = 300 \, \text{units} \]

Substitute the values of \( a \) and \( b \) into the equation and solve for \( h \):
\[ \frac{1}{2} (100 + 300) h = 5000 \]
\[ \frac{1}{2} (400) h = 5000 \]
\[ 200h = 5000 \]

Divide both sides by 200:
\[ h = \frac{5000}{200} \]
\[ h = 25 \, \text{units} \]

So, the height \( h \) of the trapezoid is 25 units.

Would you like any details or have any questions about this solution?

Here are 8 related questions:

1. What is the formula for the area of a trapezoid?
2. How do you derive the area formula for a trapezoid?
3. Can you provide an example of finding the area of a trapezoid with different base lengths?
4. How do you find the height of a trapezoid if the area and bases are known?
5. What are some real-life applications of calculating the area of a trapezoid?
6. How can you use the properties of trapezoids to solve more complex geometric problems?
7. What is the relationship between the bases and height in determining the area of a trapezoid?
8. Can you explain how the area of a trapezoid changes if one of the bases is increased or decreased?

**Tip:** Always double-check the units when solving geometry problems to ensure accuracy in your calculations.

Learn how to find the area of a trapezoid with given bases of 100 units and 300 units and an area of 5000 square units. Step-by-step solution provided with calculations and formula application.

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