Chapter MPS, Problem 4.6MPS

To determine

Find the area of the town.

Answer to Problem 4.6MPS

  $22.5k{m}^2$

Explanation of Solution

Given information:

The given points are

  $\left(3,1\right),\left(4,15\right),and\left(7,12\right)$

Calculation:

The vertices are as follows.

  $\left(3,1\right),\left(4,15\right),\left(7,12\right)$

The area of the town is calculated below.

  $\begin{array}{l}A=\frac{1}{2}\left|\begin{array}{ccc}3& 1& 1\\ 4& 15& 1\\ 7& 12& 1\end{array}\right|\\ =\frac{1}{2}\left[3\left(15-12\right)-1\left(4-7\right)+1\left(48-105\right)\right]\\ =\frac{1}{2}\left[9+3-57\right]\\ =-22.5k{m}^2\end{array}$

Hence, the area of the town is $22.5k{m}^2$ .