What is the area of a triangle with side lengths $17$, $25$, and $26$?

[i]2019 CCA Math Bonanza Lightning Round #3.2[/i]
1. **Identify the side lengths and calculate the semi-perimeter:**
   The side lengths of the triangle are \(a = 17\), \(b = 25\), and \(c = 26\).
   The semi-perimeter \(s\) is given by:
   \[
   s = \frac{a + b + c}{2} = \frac{17 + 25 + 26}{2} = \frac{68}{2} = 34
   \]

2. **Apply Heron's Formula:**
   Heron's Formula for the area \(A\) of a triangle with side lengths \(a\), \(b\), and \(c\) is:
   \[
   A = \sqrt{s(s-a)(s-b)(s-c)}
   \]
   Substituting the values we have:
   \[
   A = \sqrt{34(34-17)(34-25)(34-26)}
   \]

3. **Simplify the expression inside the square root:**
   \[
   34 - 17 = 17
   \]
   \[
   34 - 25 = 9
   \]
   \[
   34 - 26 = 8
   \]
   Therefore, the expression becomes:
   \[
   A = \sqrt{34 \times 17 \times 9 \times 8}
   \]

4. **Calculate the product inside the square root:**
   \[
   34 \times 17 = 578
   \]
   \[
   9 \times 8 = 72
   \]
   \[
   578 \times 72 = 41616
   \]

5. **Take the square root of the product:**
   \[
   A = \sqrt{41616} = 204
   \]

Thus, the area of the triangle is:
\[
\boxed{204}
\]