To find the area of Bob's triangular-shaped ice skating rink with sides of lengths 21 feet, 24 feet, and 27 feet, we can use Heron's formula.

Heron's formula states that the area of a triangle can be calculated from its side lengths $a$, $b$, and $c$ using the following steps:

1. Calculate the semi-perimeter $s$: $s = \frac{a + b + c}{2}$
2. Use the semi-perimeter to find the area $A$: $A = \sqrt{s(s-a)(s-b)(s-c)}$

Let's apply these steps:

1. Calculate the semi-perimeter $s$: $s = \frac{21 + 24 + 27}{2} = \frac{72}{2} = 36$

2. Calculate the area $A$: $A = \sqrt{36(36-21)(36-24)(36-27)}$ $A = \sqrt{36 \times 15 \times 12 \times 9}$

To simplify this calculation: $36 \times 15 = 540$ $540 \times 12 = 6480$ $6480 \times 9 = 58320$

Thus, $A = \sqrt{58320}$

Approximating the square root: $A \approx 241.43$

Rounding to the nearest square foot: $A \approx 241 \text{ square feet}$

So, the area of Bob's ice skating rink is approximately 241 square feet.

Would you like more details or have any questions?

Here are 8 related questions that expand on this information:

1. How does Heron's formula work for different types of triangles?
2. Can you calculate the height of the triangle from one of its sides?
3. What is the significance of the semi-perimeter in Heron's formula?
4. How would the area change if one of the side lengths was increased by 5 feet?
5. Can Heron's formula be used for right triangles?
6. What other methods can be used to find the area of a triangle?
7. How would you find the circumradius of this triangle?
8. How can you verify if the given side lengths form a valid triangle?

Tip: When using Heron's formula, ensure all calculations are accurate, especially when working with large numbers or decimals.