Question

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

Answer 1

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]