The area of a rhombus can be calculated using the formula: Area = (diagonal1 * diagonal2) / 2.

Let’s assume the diagonals of the rhombus are d1 and d2.

Given that the area of the rhombus is 56 m², we have:

56 = (d1 * d2) / 2

Multiplying both sides of the equation by 2, we get:

112 = d1 * d2

The perimeter of a rhombus is given by the formula: Perimeter = 4 * side length.

Given that the perimeter is 28 m, we have:

28 = 4 * side length

Dividing both sides of the equation by 4, we get:

7 = side length

Since the opposite sides of a rhombus are equal, the diagonals divide the rhombus into four congruent right-angled triangles.

Let’s consider one of these triangles. The base of the triangle is half the length of one side of the rhombus, which is 7/2 = 3.5 m.

The area of the triangle can be calculated using the formula: Area = (base * height) / 2.

Given that the area of the triangle is 56 m², we have:

56 = (3.5 * height) / 2

Multiplying both sides of the equation by 2, we get:

112 = 3.5 * height

Dividing both sides of the equation by 3.5, we get:

height = 112 / 3.5 = 32 m

Therefore, the altitude of the rhombus is 32 m.