Find the area of the triangle $A B C$. \[ a=105.9 m \quad b=89.8 m \quad c=100.6 m \] What is the area of the triangle? $\mathrm{m}^{2}$ (Round to the nearest square meter as needed)

Step 1 ：Given the sides of the triangle as: \(a = 105.9 m\), \(b = 89.8 m\), and \(c = 100.6 m\).

Step 2 ：We can use Heron's formula to find the area of the triangle. Heron's formula states that the area of a triangle with sides of length a, b, and c is \(\sqrt{s(s - a)(s - b)(s - c)}\) where s is the semi-perimeter of the triangle, calculated as \(s = \frac{a + b + c}{2}\).

Step 3 ：First, we calculate the semi-perimeter, \(s = \frac{105.9 + 89.8 + 100.6}{2} = 148.15\).

Step 4 ：Substitute the values of a, b, c, and s into Heron's formula to find the area: \(\sqrt{148.15(148.15 - 105.9)(148.15 - 89.8)(148.15 - 100.6)}\).

Step 5 ：The calculated area of the triangle is approximately 4167 square meters.

Step 6 ：Final Answer: The area of the triangle is \(\boxed{4167}\) square meters.