The diagonals of the rhombus are 2 cm and 4√2 cm. Find the length of the side of the rhombus.

Knowing the lengths of the diagonals of the rhombus, we determine its area.

Savsd = (d1 * d2) / 2 = 2 * 4 * √2 / 2 = 4 * √2 cm ^ 2.

The diagonals of the rhombus, at the point of their intersection, are halved and intersect at right angles.

Then AO = AC / 2 = 2/2 = 1 cm, BO = BD / 2 = 4 * √2 / 2 = 2 * √2 cm.

In a right-angled triangle AOB, according to the Pythagorean theorem, AB ^ 2 = AO ^ 2 + BO ^ 2 = 1 + 8 = 3.

AB = 3 cm.

Let’s define the perimeter of the rhombus.

Ravsd = 4 * AB = 4 * 3 = 12 cm.

Answer: The perimeter is 13 cm, the area is 4 * √2 cm ^ 2.