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.

To prove: area (ΔBCE) = 1/2 area (ΔACF)

Proof: Since ΔBCE and ΔACF are equilateral triangles