The formula for the area of a rhombus is given by:

Area = (diagonal1 * diagonal2) / 2

Since the formula for the area of a parallelogram is applicable to a rhombus, we can use this formula to find the area of the rhombus.

Let’s assume that 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

Now, let’s find the perimeter of the rhombus. The perimeter of a rhombus is given by:

Perimeter = 4 * side

Given that the perimeter of the rhombus is 28 m, we have:

28 = 4 * side

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

side = 7 m

Since a rhombus has equal sides, all sides of the rhombus are 7 m.

Now, let’s find the length of the diagonals. Since the diagonals of a rhombus bisect each other at right angles, we can divide the rhombus into four congruent right triangles.

Let’s consider one of these right triangles. The hypotenuse of this right triangle is the side of the rhombus, which is 7 m. The base of this right triangle is half the length of one of the diagonals, which we’ll call x.

Using the Pythagorean theorem, we have:

x² = 7² - (7/2)² x² = 49 - 24.5 x² = 24.5 x ≈ 4.95

Therefore, the length of one of the diagonals is approximately 4.95 m.

Since the diagonals of a rhombus are perpendicular bisectors of each other, the altitude of the rhombus is the length of one of the diagonals.

Therefore, the altitude of the rhombus is approximately 4.95 m.