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?

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