Answer:
[tex]\boxed{11486}[/tex]
Explanation:
1. Calculate the perimeter p
p = a + b + c = 174 + 138 + 188 = 500
2. Calculate the semiperimeter s
s = p/2 = 500/2 = 250
3. Calculate the area
We can use Heron's Formula:
[tex]\begin{array}{rcl}A & = & \sqrt{s(s-a)(s-b)(s-c)}\\& = & \sqrt{250(250-174)(250-138)(250-188)}\\& = & \sqrt{250\times 76 \times 112 \times 62}\\& = &\sqrt{131 936 000}\\& = & \mathbf{11 486}\\\end{array}[/tex]
[tex]\text{The area of the triangle is } \boxed{\textbf{11486}}][/tex]
