Find the area of the triangle $A B C$.
\[
a=340 \mathrm{~cm} \quad b=234 \mathrm{~cm} \quad c=429 \mathrm{~cm}
\]
What is the area of the triangle?
$\mathrm{cm}^{2}$
(Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.)

Step 1 ：Given a triangle ABC with side lengths a = 340 cm, b = 234 cm, and c = 429 cm.

Step 2 ：We can calculate the area of the triangle using Heron's formula, which is given by \(Area = \sqrt{s(s - a)(s - b)(s - c)}\), where s is the semi-perimeter of the triangle, calculated as \((a + b + c) / 2\).

Step 3 ：First, calculate the semi-perimeter s: \(s = (a + b + c) / 2 = (340 + 234 + 429) / 2 = 501.5\) cm.

Step 4 ：Then, substitute the values of a, b, c, and s into Heron's formula to find the area: \(Area = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{501.5(501.5 - 340)(501.5 - 234)(501.5 - 429)} = 39632.60587492955\) cm².

Step 5 ：Rounding to the nearest tenth, the area of the triangle is approximately 39632.6 cm².

Step 6 ：Final Answer: The area of the triangle is \(\boxed{39632.6}\) cm².