Know the length of the three middle lines of the triangle and find the area of the triangle Given that the lengths of the three middle lines of a triangle are 3, 4 and 5, calculate the area of the triangle How to prove that the area of triangle ABC is equal to the area of six triangle BOD?
Let ABC be a triangle with three central lines: AD, be and CF intersecting at O, and the lengths are 3, 4 and 5 respectively. Extend od to g, so that OD = dg. ∵ o is the center of gravity ∵ Ao = 2 / 3aD, OD = 1 / 3aD; Bo = 2 / 3bE, OE = 1 / 3bE; CO = 2 / 3cf, of = 1 / 3cf (textbook method) ∵ og = 2 × od = 2 × (1 / 3) ad = 6 / 3, Bo = 2