Questions: Find the area K of the triangle. K = □ square units (Round to two decimal places as needed.)

Solution Steps

The semi-perimeter $s$ is calculated as follows: $s = \frac{a+b+c}{2} = \frac{2+4+5}{2} = \frac{11}{2} = 5.5$

Heron's formula states that the area $K$ of a triangle with sides $a, b, c$ and semi-perimeter $s$ is given by:

$K = \sqrt{s(s-a)(s-b)(s-c)}$

Substituting the values we have:

$K = \sqrt{5.5(5.5-2)(5.5-4)(5.5-5)}$ $K = \sqrt{5.5(3.5)(1.5)(0.5)}$ $K = \sqrt{14.4375}$ $K \approx 3.79967$

Rounding the area to two decimal places gives:

$K \approx 3.80$

Final Answer: The final answer is $\boxed{3.80}$