A triangle has corners at #(9 ,4 )#, #(3 ,2 )#, and #(5 ,2 )#. What is the area of the triangle's circumscribed circle?

1 Answer
Binayaka C.
Jun 5, 2016

Area of the triangle's circumscribed Circle is #154.47 units^2#

Explanation:

Let a , b, c be the length of sides of the triangle; #a=sqrt((9-3)^2+(4-2)^2)=sqrt 40 = 6.32 (2dp)# #b=sqrt((3-5)^2+(2-2)^2)=sqrt 4 = 2.0 #
#c=sqrt((5-9)^2+(2-4)^2)=sqrt 20 = 4.47 (2dp)#
Semi Perimeter of the triangle #s=(6.32+2.0+4.47)/2 =6.395#
Area of the triangle #=A_t= sqrt (s(s-a)(s-b)(s-c)) = sqrt (6.395*0.075*4.395*1.925)=2.0144#
Radius of the circumscribed circle #= (a*b*c)/A_t =(6.32*2.0*4.47)/(4*2.0144)=7.012 :.#Area of the Circle #=pi* 7.012^2=154.47(2dp)#[ans]

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