Question

The length of the diagonal of a square is d units. The area of the square is
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Answer 1

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,

Hypotenuse2 = Perpendicular2 + Base2

In the above diagram,

Perpendicular = a

Base = a

Hypotenuse = d

So,

a2 + a2 = d2

⇒ 2a2 = d2

Or, a2 = d2/2

Now, area of a square = a2 = d2/2

So, area of a square using diagonals = ½ × d2 Square units.

Answer 2

the area of a square if the length of the diagonol of a square is “d” units is " d²/2"