Question

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

Answer 1

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]