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The diagonal of a square is x units. What is the area of the square in terms of x?
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Given :-

  • The diagonal of a square is x .

To Find :-

  • The area of the square in terms of x .

Solution :-

We know that in a square all the sides are equal . And hence the diagonal of the square is √2 times that of the side . So , if the diagonal is x then the side will be ,

[tex]\longrightarrow[/tex] Side = x/√2

Now again we know that the area of the square is side² . So that ,

[tex]\longrightarrow[/tex] Area = x/√2 * x/√2

[tex]\longrightarrow[/tex] Area = x * x / √2*√2

[tex]\longrightarrow[/tex] Area = x²/2

[tex]\longrightarrow[/tex] Area = 1/2 * (diagonal)²

Hence the required answer is x²/2.

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