The given information:
- Area of the rhombus = 28 cm²
- One diagonal of the rhombus = 4 cm

To find the perimeter of the rhombus, we need to know the length of the sides. However, the given information does not directly provide the length of the sides. Therefore, we need to use some properties of a rhombus to solve this problem.

Properties of a Rhombus:
1. A rhombus is a quadrilateral with all four sides of equal length.
2. The diagonals of a rhombus are perpendicular bisectors of each other, meaning they intersect at a right angle and divide each other into two equal parts.

Formula for the Area of a Rhombus:
The formula to find the area of a rhombus is:
Area = (diagonal1 * diagonal2) / 2

Using the given area, we can rearrange the formula to find the length of the other diagonal of the rhombus.

Calculating the Length of the Other Diagonal:
Area = (diagonal1 * diagonal2) / 2
28 cm² = (4 cm * diagonal2) / 2
56 cm² = 4 cm * diagonal2
diagonal2 = 56 cm² / 4 cm
diagonal2 = 14 cm

Now we have the lengths of both diagonals of the rhombus.

Calculating the Perimeter of the Rhombus:
To find the perimeter, we need the length of one of the sides of the rhombus. Since all sides of a rhombus are equal, we can use the Pythagorean theorem to find the length of one side.

Using one diagonal as the hypotenuse and half the length of the other diagonal as one of the legs, we can apply the Pythagorean theorem as follows:

(diagonal1/2)² + (diagonal2/2)² = side²
(4 cm/2)² + (14 cm/2)² = side²
2 cm² + 49 cm² = side²
51 cm² = side²
side = √51 cm

Now we have the length of one side of the rhombus, which is approximately 7.14 cm.

The perimeter of the rhombus is the sum of all four sides:
Perimeter = 4 * side
Perimeter = 4 * 7.14 cm
Perimeter = 28.56 cm

Therefore, the perimeter of the rhombus is approximately 28.56 cm.

56 cm