To find the altitude of a rhombus, we need to use the formula:

Area = (diagonal1 * diagonal2) / 2

Given that the area is 56 m², we can rewrite the formula as:

56 = (diagonal1 * diagonal2) / 2

Since a rhombus has equal diagonals, we can let d represent the length of both diagonals. Therefore, we can rewrite the formula as:

56 = (d * d) / 2

Multiplying both sides by 2, we get:

112 = d * d

Taking the square root of both sides, we find:

d = √112

Simplifying the square root, we get:

d ≈ 10.583

Since the perimeter of the rhombus is 28 m, each side length is 28 / 4 = 7 m.

Now, we can use the formula for the altitude of a rhombus:

Altitude = (2 * Area) / (diagonal1)

Substituting the given values, we have:

Altitude = (2 * 56) / 10.583

Simplifying, we find:

Altitude ≈ 10.583 m

Therefore, the altitude of the rhombus is approximately 10.583 m.