SOLUTION: Find the area of the triangle whose vertices are (3; 4) ; (-2; 5) ; (0;-6)

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Question 859411: Find the area of the triangle whose vertices are (3; 4) ; (-2; 5) ; (0;-6)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Calculate the distances between the points.
D%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2
.
.
D%5B1%5D%5E2=%28-2-3%29%5E2%2B%285-4%29%5E2=25%2B1=26
D%5B1%5D=sqrt%2826%29
D%5B2%5D%5E2=%280-%28-2%29%29%5E2%2B%28-6-5%29%5E2=4%2B121=125
D%5B2%5D=5%2Asqrt%285%29
D%5B3%5D%5E2=%283-0%29%5E2%2B%284-%28-6%29%29%5E2=9%2B100=109
D%5B3%5D=sqrt%28109%29
Use Heron's formula,
p=%28D%5B1%5D%2BD%5B2%5D%2BD%5B3%5D%29%2F2
p=%28sqrt%2826%29%2B5%2Asqrt%285%29%2Bsqrt%28109%29%29%2F2
A=sqrt%28p%28p-D%5B1%5D%29%28p-D%5B2%5D%29%28p-D%5B3%5D%29%29
A=53%2F2