Chapter MPS, Problem 4.7MPS

To determine

Find the area of the forest.

Answer to Problem 4.7MPS

  $287.5m{i}^2$

Explanation of Solution

Given information:

He lays a coordinate grid in which $1unit=10miles$ over a map of the forest with the origin at the entrance to the park. The coordinates of the two other exists are $\left(7,5\right)and\left(25,10\right)$ .

Calculation:

The vertices are as follows.

  $\left(0,0\right),\left(7,5\right),\left(2.5,10\right)$

The area of the forest is calculated below.

  $\begin{array}{l}A=\frac{1}{2}\left|\begin{array}{ccc}0& 0& 1\\ 7& 5& 1\\ 2.5& 10& 1\end{array}\right|\\ =\frac{1}{2}\left[0\left(5-10\right)-0\left(7-2.5\right)+1\left(70-12.5\right)\right]\\ =\frac{1}{2}\left[0-0+57.5\right]\\ =28.75uni{t}^2\end{array}$

The area in miles is calculated below.

  $\begin{array}{l}28.75\times 10\\ =287.5m{i}^2\end{array}$

Hence, the area of the forest is $287.5m{i}^2$ .