In triangle ABC ,D and E are the mid points of BC and AC respectively prove that the area of triangle ABC is 4 times than triangle ABE

Answer 1

By the midpoint theorem, DE = (1/2)AB and DE || AB
so we have similar triangles EDC and ABC

let the altitude from C to DE be h
then by similar triangles the altitude from C to AB = 2h
and AB = 2DE

area of triangle DEC = (1/2)(DE)h
area of triangle ABC = (1/2)(AB)(2h)
= (1/2)(2DE)(2h
= 2(DE)h = 4[ (1/2)(DE)h ]