A triangle has corners at #(5 ,3 )#, #(2 ,4 )#, and #(7 ,2 )#. What is the area of the triangle's circumscribed circle?

1 Answer
Jul 13, 2016

Area of circumscribed circle is #1502.48(2dp)# sq unit

Explanation:

Side #A=sqrt((5-2)^2+(3-4)^2) = sqrt10=3.16#
Side #B=sqrt((2-7)^2+(4-2)^2) = sqrt29=5.39#
Side #B=sqrt((7-5)^2+(2-3)^2) = sqrt5=2.24#
Semi perimeter #s=(3.16+5.39+2.24)/2 =5.395#
Area #A_r=sqrt(5.395(5.395-3.16)(5.395-5.39)(5.395-2.24))=0.436#
Radius of circumscribed circle is #(A*B*C)/(4*A_r) =(3.16*5.39*2.24)/(4*0.436) =21.869#
Area of circumscribed circle is #pi*21.869^2=1502.48(2dp)#sq unit[Ans]