Question 859411
{{{drawing(300,300,-8,8,-8,8,grid(1),circle(3,4,0.3),circle(-2,5,0.3),circle(0,-6,0.3),line(3,4,-2,5),line(-2,5,0,-6),line(0,-6,3,4))}}}
Calculate the distances between the points.
{{{D^2=(x[2]-x[1])^2+(y[2]-y[1])^2}}}
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{{{D[1]^2=(-2-3)^2+(5-4)^2=25+1=26}}}
{{{D[1]=sqrt(26)}}}
{{{D[2]^2=(0-(-2))^2+(-6-5)^2=4+121=125}}}
{{{D[2]=5*sqrt(5)}}}
{{{D[3]^2=(3-0)^2+(4-(-6))^2=9+100=109}}}
{{{D[3]=sqrt(109)}}}
Use Heron's formula,
{{{p=(D[1]+D[2]+D[3])/2}}}
{{{p=(sqrt(26)+5*sqrt(5)+sqrt(109))/2}}}
{{{A=sqrt(p(p-D[1])(p-D[2])(p-D[3]))}}}
{{{A=53/2}}}