Question

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

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Answer 1

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 ,

`\longrightarrow` Side = x/√2

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

`\longrightarrow` Area = x/√2 * x/√2

`\longrightarrow` Area = x * x / √2*√2

`\longrightarrow` Area = x²/2

`\longrightarrow` Area = 1/2 * (diagonal)²

Hence the required answer is x²/2.