The midpoints of the sides of a triangle along with any of the vertices as the fourth point makes a parallelogram of area equal to

Question

Philoid · Accepted Answer

Join EF

Here Area (ΔAEF) = Area (ΔBDF) = Area (ΔDEF) = Area (ΔDEC) = Area (ΔABC) – 1

Consider any vertex of the triangle.

Let us consider Vertex B

Here, BDEF form a parallelogram.

Area (||gm BDEF) = Area (ΔBDF) + Area (ΔDEF)

Area (||gm BDEF) = Area (ΔABC) + Area (ΔABC) = Area (ΔABC) (from –1)

∴ Area (||gm BDEF) = Area (ΔABC)

Similarly, we can prove for other vertices.