Paragraph : The vertices of a triangle A B C are A(2,3,1), B(-2,2,0) and C(0,1,-1) . Question : What is the area of the triangle?

Step-by-step solution

aligned & a= BC = (2)^2+(-1)^2+(-1)^2 = 4+1+1 = 6 & b= CA = (2)^2+(2)^2+(2)^2 = 4+4+4 = 12 & c= AB = (4)^2+(1)^2+(1)^2 = 16+1+1 = 18 . aligned aligned C & = a^2+b^2-c^2 2 a b & = 6+12-18 2 6 12 =0 C & = 90^ C =90^ aligned It is right triangle. Area of aligned ABC & = 1 2 base height & = 1 2 6 12 = 1 2 72 & = 1 2 6 2 =3 2 square unit. aligned