Question

Find the area, in square units, of AABC plotted below.

C(-6,-2)
D(-7,-5) d
A(-4,-6)
B(2,-8)

Answer 1

Check the picture below.

so the base of that triangle is AB whilst the height of it is CD, so let's get them

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{-8})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ AB=√((~~2 - (-4)~~)^2 + (~~-8 - (-6)~~)^2) \implies AB=√((2 +4)^2 + (-8 +6)^2) \\\\\\ AB=√(( 6 )^2 + ( -2 )^2) \implies AB=√( 36 + 4 ) \implies AB=√( 40 )\implies \stackrel{base}{AB=2√(10)} \\\\[-0.35em] ~\dotfill`

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ C(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad D(\stackrel{x_2}{-7}~,~\stackrel{y_2}{-5})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ CD=√((~~-7 - (-6)~~)^2 + (~~-5 - (-2)~~)^2) \\\\\\ CD=√((-7 +6)^2 + (-5 +2)^2) \\\\\\ CD=√(( -1 )^2 + ( -3 )^2) \implies CD=√( 1 + 9 ) \implies \stackrel{height}{CD=√( 10 )} \\\\[-0.35em] ~\dotfill`

`A=\cfrac{1}{2}(\stackrel{b}{2√(10)})(\stackrel{h}{√(10)})\implies A=√(10)\cdot √(10)\implies A=√(10^2)\implies {\Large \begin{array}{llll} A=10 \end{array}}`