Answer
$A = 9$
Work Step by Step
$$\eqalign{
& {\text{Let the points }}A\left( {0,0} \right),{\text{ }}B\left( {6,0} \right){\text{ and }}C\left( {4,3} \right) \cr
& {\text{*Find the equation of the line between the points }}A{\text{ and }}C \cr
& y - {y_1} = m\left( {x - {x_1}} \right) \cr
& y + 0 = \frac{{3 - 0}}{{4 - 0}}\left( {x - 0} \right) \cr
& y = \frac{3}{4}x \cr
& \cr
& {\text{*Find the equation of the line between the points }}C{\text{ and }}B \cr
& y - {y_1} = m\left( {x - {x_1}} \right) \cr
& y = \frac{{3 - 0}}{{4 - 6}}\left( {x - 6} \right) \cr
& y = - \frac{3}{2}x + 9 \cr
& \cr
& {\text{From the image shown below}}{\text{, we can define the area as}} \cr
& A = \int_0^4 {\frac{3}{4}xdx + \int_4^6 {\left( { - \frac{3}{2}x + 9} \right)dx} } \cr
& {\text{Integrate and evaluate}} \cr
& A = \left[ {\frac{3}{8}{x^2}} \right]_0^4 + \left[ { - \frac{3}{4}{x^2} + 9x} \right]_4^6 \cr
& A = \frac{3}{8}{\left( 4 \right)^2} - \frac{3}{4}{\left( 6 \right)^2} + 9\left( 6 \right) + \frac{3}{4}{\left( 4 \right)^2} - 9\left( 4 \right) \cr
& {\text{Simplifying}} \cr
& A = 9 \cr} $$
