Calculate the area of a square KLMN if the diagonal of the square is 20 dm.

univerkov | March 11, 2021 | education

The first way.

The area of a square is half the square of its diagonal.

Skv = KM ^ 2/2 = 400/2 = 200 dm2.

Second way.

All sides of a square are equal, then, by the Pythagorean theorem, KM ^ 2 = 2 * KL ^ 2.

KL ^ 2 = KM ^ 2/2 = 400/2 = 200.

КL = 10 * √2.

Then Sкм = КL ^ 2 = (10 * √2) ^ 2 = 200 dm2.

Answer: The area of the square is 200 dm2.

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