Question

In ∆UVW, u=140cm, u=176 cm and w=750cm. find the area of ∆UVW to the nearest 10th of a square centimeter.

Answer 1

Step 1: Problem

Step 2: Concept

Apply heron formula

`\begin{gathered} s\text{ = }\frac{u\text{ + v + w}}{2} \\ \text{Area = }\sqrt[]{s(s-u)(s-v)(s-w)} \end{gathered}`

Step 3: Method

u = 140 v = 760 w = 750

`\begin{gathered} s\text{ = }\frac{140\text{ + 760 + 750}}{2} \\ s\text{ = }(1650)/(2) \\ s\text{ = 825} \end{gathered}`
`\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 }*\text{ 65 }*\text{ 75}} \\ =\text{ }\sqrt[]{2754984375} \\ =52487.9cm^2 \end{gathered}`

Step 4: Final answer

Area of triangle UVW = 52487.9