Question

the area of the square having diagonal of length d is given by​

Answer 1

it can easily done with phythagoras because as we know all angles of a square are 90 degree Please check the explanation above

Answer 2

Answer:

$Area of square = \frac{1}{2} * d^{2}Square units$

Step-by-step explanation:

In the  figure, the square of the side “a” unit, has been divided into two right triangles with the help of diagonal of length “d” units. Thus, the diagonal of the square divides it into two right triangles. Consider any right triangle and apply Pythagoras theorem.

According to Pythagoras theorem, for a right-angled triangle,

$Hypotenuse^{2} = Perpendicular^{2} + Base^{2}$

In the diagram,

Perpendicular = a, Base = a, Hypotenuse = d

So,

$d^{2}= a^{2}+ a^{2}$

$d^{2} =2a^{2}$

$a^{2} = \frac{d^{2} }{2}$

Area of a square ,$a^{2} = \frac{d^{2} }{2}$.

So, area of a square using diagonals = $\frac{1}{2} *d^{2}$Square units.