And Bde Are Two Equilateral Triangles Such That Mid Point Then Prove That Area В–Іbde Area В–Іabc

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then prove that area (△BDE) = 1/4 area (△ABC)


Solution   :-

Let the side of triangle, BC = a ⇒  BD = a/2

          area(△BDE) = 3/4 (a/2)2

                                         = √3/4.a2/4 = 1/4 (√3/4.a2)

             area(BDE )    = 1/4 area (ABC)