[1] Step 1: Find the Area of the Triangle
Use Heron's formula: #Area_triangle=sqrt(s(s-a)(s-b)(s-c))#
where #a, b, c# are the lengths of the sides and #s# is the semi-perimeter #(a+b+c)/2#
#color(white)("XXX")s=(5+7+3)/2=15/2#
#color(white)("XXX")Area_triangle = sqrt(15/2 * 5/2 * 1/2 * 9/2)#
#color(white)("XXXXXXX")=15/4sqrt(3)#
[2] Step 2: Find the Radius of Inscribed Circle
Use teh forumla: #"Radius"_circ = "Area"_triangle/s#
#color(white)("XXXXXXXXX")#If you are unfamiliar with this formula:
#color(white)("XXXXXXXXX")#ask to have it explained as a separate question.
#color(white)("XXX")r_circ = (15/4sqrt(3))/(15/2)=sqrt(3)/2#
~~~~~~ Oops! The next step wasn't asked for but I did it anyway ~~~~~
[3] Calculate the Area of the Circle
Use the formula: #"Area"_circ = pir^2#
#color(white)("XXX")"Area"_circ = pi(sqrt(3)/2)^2=3/4pi#
