Find the area of a square if its diagonals are 20 cm.

1. Vertices of the square A, B, C, D. S – the area of the square. Diagonals of the square AC = ВD = 20 centimeters.
2. All sides of the square are equal. Take x as the length of the side of the square.
3. We draw up an equation using the formula of the Pythagorean theorem:
x² + x² = AC².
2x² = 20² = 400.
x² = 400/2.
x = √400 / 2 = 20 / √2 = 10√2 centimeters.
The length of each side of the square (AB, BC, СD, AD) is 10√2 centimeters.
4. S = 10√2 x 10√2 = 100 x 2 = 200 centimeters².
Answer: S equals 200 centimeters².