Prove that area of equilateral triangle on one side of a square is equal to half area of equilateral triangle on one of its diagonals.

Question

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

Answer 1

Let ABCD be a square and ΔBCE and ΔACF have been drawn on side BC and the diagonal AC respectively.