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.

Given: ABCD is a Square, DB is a diagonal of square, △DEB and △CBF are Equilateral Triangles.
To Prove: A(△CBF)/A(△DEB) = 1/2
Proof:
Since, △DEB and △CBF are Equilateral Triangles.
∴Their corresponding sides are in equal ratios.
In a Square ABCD, DB = BC√2 (1)
∴A(△CBF)/A(△DEB) = (√3/4 × (BC)²)/(√3/4 × (DB)²)
∴A(△CBF)/A(△DEB) = (√3/4 × (BC)²)/(√3/4 × (BC√2)²) (From 1)
∴A(△CBF)/A(△DEB) = 1/2