# The side of a square is 8 cm. Find the area of the square drawn on a diagonal of the original square (8 cm X 8 cm).

## Expert Answers You need to find the length of side of the new square whose area you need to evaluate, hence, using the information provided by the problem, that the side of the new square is the diagonal of the original square, you need to remember the equation that relates the side of a square and its diagonal, such that:

`d = l sqrt 2`

`d` represents the length of diagonal of square

`l` represents the length of the side of the square

You need to evaluate the area of the new square, such that:

`A = d*d => A = d^2 => A = (l*sqrt 2)^2 => A = 2l^2`

You need to substitute `8 cm` for `l `  such that:

`A = 2*64 cm^2 => A = 128 cm^2`

Hence, evaluating the area of the new square, yields `A = 128 cm^2.`

Approved by eNotes Editorial Team

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