Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.)
\[
a=5.7, b=11.1, c=8
\]
\(\boxed{21.80}\) is the final answer.
Step 1 :Given the lengths of the sides of the triangle as \(a = 5.7\), \(b = 11.1\), and \(c = 8\).
Step 2 :We can calculate the semi-perimeter of the triangle, \(s\), using the formula \(s = \frac{a + b + c}{2}\). Substituting the given values, we get \(s = 12.4\).
Step 3 :Next, we can find the area of the triangle using Heron's formula: \(Area = \sqrt{s(s - a)(s - b)(s - c)}\).
Step 4 :Substituting the values of \(s\), \(a\), \(b\), and \(c\) into the formula, we get \(Area = 21.799486232478056\).
Step 5 :Rounding to two decimal places, the area of the triangle is \(21.80\) square units.
Step 6 :\(\boxed{21.80}\) is the final answer.