Question

the diagonal of a square field is 90 M what is its area

Answer 1

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→area of square = side *side

→as diagonal is given , so we can use another formula of area of square

→ area of square=$\frac{ d^{2} }{2}$

⇒where d is diagonal

⇒so,  90²÷2
⇒ 8100/2
⇒4050 $m^{2}$

∴ your answer is 4050 $m^{2}$

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Answer 2

Let the square be ABCD whose each side measures 'x '.

The two perpendiculars are AC and BD.

AB = BD = 90 m (diagnols of a square are equal in length).

In triangle ABC , angle B = 90° (all angles of a square are right angles).

(Use Pythagoras theorem)

AC² = AB² + BC²

(90 m)² = (x )² + (x )²

2x² = 8100 m²

x² = 4050 m²..........1

Area of a square = side²

= x²

Substitute the value of x² from eq 1

= 4050 m²

Ans. = 4050 m²

Hope it helps! ^^