Chapter 8.5, Problem 22E

To determine

Use a graphing utility to find the area (in square feet) of the region.

Answer to Problem 22E

  $\boxed{{3100}^{2}feet}$

Explanation of Solution

Given information:

A botanist is studying the plants growing in the triangular region shown in the figure. Starting at vertex $A$ , the botanist walks $65$ feet east and $50$ feet north to vertex $B$ , and then walks $85$ feet west and $30$ feet north to vertex $C$ . Use a graphing utility to find the area (in square feet) of the region.

  

Calculation:

Consider the figure for directions,

  

vertex be $\left(0,0\right)$ , $\left(65,50\right)$ and $\left(-20,80\right)$ from the figure,

Now obtained the determinant,

  $D=\left|\begin{array}{ccc}0& 0& 1\\ 65& 50& 1\\ -20& 80& 1\end{array}\right|$

Enter the matrix on the graphic calculator,

Press $2nd$ and then $X^{-1}$ , the display is as shown,

  

Scroll to EDIT and choose $1$ and press ENTER.

Now enter the number of rows and column and press ENTER.

  

Enter the matrix elements,

  

Press $2nd$ and MODE to EXIT. Press $2nd$ and $X^{-1}$ and scroll to MATH option and select $1$ to find the determinant of the matrix.

  

Now press ENTER,

  

To enter the name of matrix again press $2nd$ and $X^{-1}$ select $1$ and press ENTER

  

To find the value of determinant press ENTER.

  

Find the area of tract land as shown,

  

Hence area of the tract land is $\boxed{{3100}^{2}feet}$