Question

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◆●SHoW THAt ThE ARea Of A SqUARe iS EQuaL tO HaLf Of Its Length◆●

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Answer 1

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Let us take A square so called ABCD

side = x units

Diagonals AC = BD = y units

we know that when diagonals interesect each other they bisect each other at 90 degrees

AOB = 90

OA = OB = y/2 units

$\huge \frac{y {}^{2} }{4} + \frac{x {}^{2} }{4} = x {}^{2}$

Area of square = side^2

= x^2

put x^2 = y^2 / 2

Area of square =

$\frac{y {}^{2} }{2} = \frac{1}{2} \times y \times y = \frac{1}{2} \times AC \times BD$

Hence proved half of the diagonals

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Answer 2

Hope it helps you mate ! !