# Prove that the area of the square is half the square of the diagonal.

July 29, 2021 | education

| The side of the square path will correspond to the variable n.

Consequently, its area, based on the well-known formula, can be represented through n ^ 2.

Now it is necessary to express the diagonal of the square (variable d) through its side, for which we will use the Pythagorean formula known from the school course:

d ^ 2 = n ^ 2 + n ^ 2;

d ^ 2 = 2n ^ 2.

As we remember, S = n ^ 2, we substitute the area in the expression obtained above:

d ^ 2 = 2S.

Then:

d ^ 2 = 2S;

S = d ^ 2/2.

That is, we got the expression that was required in the condition.

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