Question

In (triangle)ABC , D,E F are the midpoints of BC,CA AB respectively .if ar(triangle ABC)=56 cm2 then ar(AEDF) =
Options Are -
A) 21Cm2
B)28Cm2
C)16Cm2
D) 14Cm2

Answer 1

b)28 cm square is the right answer

Answer 2

Answer:

△AEF ≅ △BDF ≅ △DEF ≅ △CDE

∴ ar(△AEF) = ar(△BDF) = ar (△DEF) = ar((△CDE)

∴ ar(△AEF) = 1/4 ar(△ABC) = 1/4 × 56 = 14 cm2

∵ Diagonals of a parallelogram divide it in two triangles having same area.

∴ ar(|| gm AEDF) = 2 × ar(△AEF)

= 2 × 14 = 28cm2