Isosceles trapezoid with bases 13 and 17, legs 8, and height h.

Let’s solve this step by step.

We have a trapezoid with:
- Top base = 13
- Bottom base = 17
- Two equal slanted sides = 8 each
- Height = h (what we need to find)
- The bottom base is split into three parts: x, 13, and x → so total bottom base = x + 13 + x = 2x + 13

But we know the bottom base is 17, so:

Step 1: Find x

2x + 13 = 17
Subtract 13 from both sides:
2x = 4
Divide by 2:
x = 2

So each small triangle on the side has a base of 2.

Step 2: Use Pythagoras to find h

Each side triangle is a right triangle with:
- Base = x = 2
- Hypotenuse = 8 (the slanted side)
- Height = h (same as the height of the trapezoid)

Pythagorean theorem:
(base)² + (height)² = (hypotenuse)²
→ 2² + h² = 8²
→ 4 + h² = 64
Subtract 4 from both sides:
h² = 60
Take square root:
h = √60

Simplify √60:
√60 = √(4 × 15) = √4 × 15 = 2√15

So h = 2√15

But let’s check if they want a decimal or exact form. Since no instruction, we can leave it as simplified radical.

Wait — maybe we should double-check calculations.

Check:
x = 2 → correct because 2+13+2=17 ✔️
Then in right triangle: legs 2 and h, hypotenuse 8 → 2² + h² = 64 → h²=60 → h=√60=2√15 ✔️

Yes, that’s correct.

Final Answer:
2√15