Circle area formula: Radius of circle inscribed

Radius of circle inscribed in a triangle = A s Where, A = Area of triangle, s =Semi-perimeter of triangle = a + b + c 2 Note a,b,c are sides of the triangle So, s = 3 +9 +7 2 = 19 2 = 9.5 We can find the area of triangle using Heron's formula : Heron's formula : Area = √s(s − a)(s − b)(s −c) → Area = √9.5(9.5 −3)(9.5 −9)(9.5 − 7) Area = √9.5(6.5)(0.5)(2.5) Area = √9.5(8.12) Area = √77.14 = 8.78 Radius = A s = 8.78 9.5 = 0.92... Area of circumscribed circle is 194.5068 If the sides of a triangle are a, b and c, then the area of the triangle Delta is given by the formula Delta=sqrt(s(s-a)(s-b)(s-c)), where s=1/2(a+b+c) and radius of circumscribed circle is (abc)/(4Delta) Hence let us find the sides of triangle formed by (4,6), (2,9) and (8,4). This will be surely distance between pair of points, which is a=sqrt((2-4)^2+(9-6)^2)=sqrt(4+9)=sqrt13=3.6056 b=sqrt((8-2)^2+(4-9)^2)=sqrt(36+25)=sqrt61=7.8102 and c=sqrt((8-4 ... The area of a circle of radius r is given by the well known formula : A = πr2 If the diameter is d the we have d = 2r ⇒ r = d 2, thus we have: A = π(d 2)2 = πd2 4 Thus, we have: d = 4 ⇒ A = π42 4 = 4π d = 9 ⇒ A = π92 4 = 81 4 π d = 11 ⇒ A = π112 4 = 121 4 π The surface area of a general ellipsoid cannot be expressed exactly by an elementary function. However an approximate formula can be used and is shown below: