Question

How to find area of square if it's diagonals are given?​

Answer 1

Answer:

Area of Square = ½ × d², where d=diagonal

hope it helps

Answer 2

Answer:

area of square if a diagonal is given

a= 1/2 x d square

Step-by-step explanation:

According to Pythagoras theorem, for a right-angled triangle,  Hypotenuse^2 = Perpendicular^2 + Base^2

(this is because a diagonal divides the square into two triangles)

now, perpendicular= a

base= a ( because all sides of square is equal)

and hypotenuse= d (diagonal)

d^2= a^2 + a^2   (from Hypotenuse^2 = Perpendicular^2 + Base^2)

⇒ 2a^2 = d^2

Or, a^2 = d^2/2

Now, area of a square = a^2 = d^2/2

So, area of a square using diagonals = ½ × d^2