Find the area of a square if its diagonal is 21.

The area of a square is equal to the product of its sides, and since the sides of a square are equal, its area is equal to the square of its side. S = a ^ 2.

Find the side of the square. The sides of the square and its diagonal form a right-angled triangle. The sides of the square are the legs of the triangle, and the diagonal of the square is the hypotenuse of the triangle. By the Pythagorean theorem: The square of the hypotenuse is equal to the sum of the squares of the legs, we have:

a ^ 2 + a ^ 2 = 21 ^ 2;

2a ^ 2 = 441;

a ^ 2 = 441/2;

a ^ 2 = 220.5;

a = √220.5.

Find the area of the square.

S = a ^ 2 = 220.5.

Answer. 220.5.