https://r2.erweima.ai/mathbot/image/1727230492646uxgjpdvo.jpg

We need to find the height of the isosceles trapezoid in the image. 

Here are the given dimensions:
- The length of the shorter base is \(5 \, \text{cm}\).
- The length of the longer base is \(13 \, \text{cm}\).
- The non-parallel sides (legs) are both \(5 \, \text{cm}\).

### Steps to solve:
1. **Difference between the bases**: The difference between the longer base and the shorter base is:
   \[
   13 \, \text{cm} - 5 \, \text{cm} = 8 \, \text{cm}
   \]
   This difference is shared equally by the two right triangles formed when we drop perpendiculars from the ends of the shorter base to the longer base. Therefore, each triangle has a horizontal leg of:
   \[
   \frac{8}{2} = 4 \, \text{cm}
   \]

2. **Using the Pythagorean theorem**: The legs of the right triangles are:
   - One leg is the height of the trapezoid (which we need to find).
   - The other leg is \(4 \, \text{cm}\) (calculated above).
   - The hypotenuse is \(5 \, \text{cm}\) (the length of the non-parallel sides).

   Applying the Pythagorean theorem:
   \[
   h^2 + 4^2 = 5^2
   \]
   \[
   h^2 + 16 = 25
   \]
   \[
   h^2 = 25 - 16 = 9
   \]
   \[
   h = \sqrt{9} = 3 \, \text{cm}
   \]

So, the height of the trapezoid is \(3 \, \text{cm}\).

The correct answer is \( \boxed{3 \, \text{cm}} \).

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

Here are 5 related questions for practice:
1. What is the area of the trapezoid?
2. How do you calculate the perimeter of the trapezoid?
3. What is the height if the non-parallel sides were 6 cm instead of 5 cm?
4. Can you derive the height if the longer base were 14 cm and the legs were still 5 cm?
5. How would the height change if the trapezoid were not isosceles but scalene?

**Tip:** The Pythagorean theorem is very useful for finding missing sides in right triangles formed inside polygons.

Encuentra la altura de este trapecio isósceles, con una base mayor de 13 cm, una base menor de 5 cm, y lados no paralelos de 5 cm.

Learn how to find the height of an isosceles trapezoid with a 13 cm base, 5 cm base, and 5 cm non-parallel sides using the Pythagorean theorem. Detailed step-by-step solution included for students in Grades 8-10.

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