Answer
$7,000,000ft^2$
Work Step by Step
Step 1. Use the figure given in the Exercise to identify the coordinates of the vertices of the triangle: $(1000,2000),(2000, 6000),(5000,4000)$.
Step 2. Use the determinant formula for the triangle area:
$\begin{array}( \\A=\pm\frac{1}{2} \\ \\ \end{array}
\begin{vmatrix} 1000&2000&1\\2000&6000&1\\5000&4000&1 \end{vmatrix}$
Step 3. Do the row operations: $R_2-R_1\to R_2, R_3-R_1\to R_3$
$\begin{array}( \\A=\pm\frac{1}{2} \\ \\ \end{array}
\begin{vmatrix} 1000&2000&1\\1000&4000&0\\4000&2000&0 \end{vmatrix}$
Step 4. Expand using column3:
$A=\frac{1}{2}|1000\times2000-4000\times4000|=7000000ft^2$
