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

Area = (diagonal1 * diagonal2) / 2

Given that the area is 56 m², we can set up the equation:

56 = (diagonal1 * diagonal2) / 2

Since the diagonals of a rhombus are perpendicular bisectors of each other, we can use the Pythagorean theorem to find the length of one of the diagonals.

Let’s assume that the length of one diagonal is x. Then the other diagonal will also be x.

Using the Pythagorean theorem, we have:

(x/2)^2 + (x/2)^2 = (28/2)^2

Simplifying the equation, we get:

x^2/4 + x^2/4 = 14^2

Combining like terms, we have:

2x^2/4 = 196

Simplifying further, we get:

x^2/2 = 196

Multiplying both sides by 2, we have:

x^2 = 392

Taking the square root of both sides, we have:

x = √392

Simplifying the square root, we get:

x ≈ 19.8

Since the altitude of a rhombus is the perpendicular distance between any two parallel sides, we can use the formula:

Altitude = (2 * Area) / Perimeter

Substituting the given values, we have:

Altitude = (2 * 56) / 28

Simplifying the equation, we get:

Altitude = 112 / 28

Altitude = 4

Therefore, the altitude of the rhombus is 4 m.