Question 660121
this is your triangle:

{{{drawing( 600, 600, -15, 15, -15, 15, 
         grid(1),
         (triangle( 1, 10, 8, 1, 13, 1 )), 
  (locate( 1,10,A(1,10))), locate(8,1,B(8,1)), locate( 13,1,C(13,1))) ) )
)}}}


now find the area:

{{{A=(1/2)ah}}} ...where {{{a}}} is the base (in your case {{{BC}}}) and {{{h}}} is the height

as you can see, we need to calculate {{{BC}}} using distance formula:

*[invoke Distance_Formula_for_Coordinate_Plane 8, 1, 13, 1]


so, {{{BC=5}}}

now, we need {{{h}}}: as you can see from the graph, {{{h}}} will be a vertical line from the point {{{A}}} to the point whose {{{y}}} coordinate is {{{1}}}
since {{{y}}} coordinate of the point {{{A}}} is {{{y=10}}}, wee will go {{{9}}} units to get in {{{y=1}}}

so, {{{h=9}}}

now we can calculate {{{A=(1/2)ah}}}


{{{A=(1/2)5*9}}}

{{{A=(1/2)45}}}

{{{A=22.5units^2}}}