Chapter 12, Problem 11CT

To determine

Find the area of triangular plot of land whose sides are $200m,150m\text{ and }100m$ .

Answer to Problem 11CT

The area of triangular plot is $7261.8{\text{ m}}^2$ .

Explanation of Solution

Given information: The given triangular plot has sides $200m,150m\text{ and }100m$ .

Calculation: The semi-perimeter of triangular plot is evaluated as,

  $\begin{array}{c}s=\frac{a+b+c}{2}\\ =\frac{200+150+100}{2}\mathrm{....}\left\{\begin{array}{l}200m,150m\\ \text{and }100m\end{array}\right\}\\ =225m\end{array}$

Now from Hero’s formula,

  $\begin{array}{c}A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\\ =\sqrt{225\left(225-200\right)\left(225-150\right)\left(225-100\right)}\mathrm{....}\left\{\begin{array}{l}\text{Sides }200m,150m,\\ 100m\text{ and }s=225\end{array}\right\}\\ =7261.8{\text{ m}}^2\end{array}$