Answer:
The area of the triangle is of 21 units of area.
Step-by-step explanation:
The area of a triangle with three vertices [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] is given by the determinant of the following matrix:
[tex]A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|[/tex]
In this question:
Vertices (3,0) (9,0) (7,6). So
[tex]A = \pm 0.5 \left|\begin{array}{ccc}3&0&1\\9&0&1\\7&7&1\end{array}\right|[/tex]
[tex]A = \pm 0.5(3*0*1+0*1*7+1*9*7-0*7*1-0*9*1-3*1*7)[/tex]
[tex]A = \pm 0.5*(63-21)[/tex]
[tex]A = \pm 0.5*42 = 21[/tex]
The area of the triangle is of 21 units of area.
