Step 1: Problem
Step 2: Concept
Apply heron formula
[tex]\begin{gathered} s\text{ = }\frac{u\text{ + v + w}}{2} \\ \text{Area = }\sqrt[]{s(s-u)(s-v)(s-w)} \end{gathered}[/tex]Step 3: Method
u = 140 v = 760 w = 750
[tex]\begin{gathered} s\text{ = }\frac{140\text{ + 760 + 750}}{2} \\ s\text{ = }\frac{1650}{2} \\ s\text{ = 825} \end{gathered}[/tex][tex]\begin{gathered} \text{Area = }\sqrt[]{s(s-u)(s-v)(s-w)} \\ =\text{ }\sqrt[]{825(825-140)(825-760)(825-750)} \\ =\text{ }\sqrt[]{825\text{ x 685 }\times\text{ 65 }\times\text{ 75}} \\ =\text{ }\sqrt[]{2754984375} \\ =52487.9cm^2 \end{gathered}[/tex]Step 4: Final answer
Area of triangle UVW = 52487.9
