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

Solution:

Let the side of the square be ‘a’ units, as shown in the figure below,

area of the square given the diagonal 'x'

By Pythagoras theorem,

a2 + a2 = x2

2a2 = x2

a2 = x2/2

a = x/√2

The area of the square = a × a

= x/√2 × x/√2

= x2/2

Therefore, the area of the square = a × a = x2/2

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

Summary:

Given the diagonal of a square of x units, the area of the square in terms of x is x2/2.

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