Question

Prove that the area of an equilateral traingle describe on one side of a square is equal to half the area of the equilateral triangle describe on one its diagnol

Answer 1

Let the side of Square be x.
Area of equilateral traingle describe on one side of a square=√3a²/4
We know that,diagonal of square=√2a
Area of equilateral triangle describe on diagonal=√3/4×2a²
=2√3a²/4
Area of equilateral triangle describe on side of square/Area of equilateral triangle describe on diagonal=√3a²/4/2√3a²/4
=1/2

Answer 2

plz refer to this attachment