The given diagram represents two identical trapezoids, one labeled ABCD (Penny's pool) and the other EFGH (Ben's pool). The lengths provided in trapezoid ABCD can be used to find the missing length of side EF in trapezoid EFGH.

Here are the lengths for trapezoid ABCD:

• $AB = 5.8 \, \text{ft}$
• $BC = 6 \, \text{ft}$
• $CD = 5.3 \, \text{ft}$
• $AD = 10 \, \text{ft}$

Since Ben’s pool is identical to Penny’s but rotated, the lengths of corresponding sides are equal. Therefore, side $EF$ in trapezoid EFGH corresponds to side $CD$ in trapezoid ABCD.

Thus, the length of side $EF$ is: $EF = CD = 5.3 \, \text{ft}$

Let me know if you'd like further details or if you have any questions!

Here are five related questions to expand your understanding:

1. What is the area of trapezoid ABCD using the given dimensions?
2. How do you calculate the perimeter of trapezoid ABCD?
3. If you rotated the trapezoid, would its properties change?
4. What is the difference between a trapezoid and a parallelogram in terms of side lengths and angles?
5. How can you find the height of a trapezoid if only the side lengths are given?

Tip: In geometry, corresponding sides and angles of identical shapes are always equal, even when the shapes are rotated or flipped!