Let’s assume the base of the parallelogram is b and the altitude is h.

The formula for the area of a parallelogram is A = b * h.

Given that the area is 56 m², we have 56 = b * h.

The formula for the perimeter of a parallelogram is P = 2 * (b + h).

Given that the perimeter is 28 m, we have 28 = 2 * (b + h).

Simplifying the equation, we have 14 = b + h.

Now we have a system of equations: 56 = b * h 14 = b + h

We can solve this system of equations by substitution.

Rearranging the second equation, we have h = 14 - b.

Substituting this value of h into the first equation, we have 56 = b * (14 - b).

Expanding the equation, we have 56 = 14b - b².

Rearranging the equation, we have b² - 14b + 56 = 0.

Factoring the equation, we have (b - 4)(b - 10) = 0.

Setting each factor equal to zero, we have b - 4 = 0 or b - 10 = 0.

Solving for b, we have b = 4 or b = 10.

If b = 4, then h = 14 - 4 = 10.

If b = 10, then h = 14 - 10 = 4.

Therefore, the possible values for the base and altitude are b = 4, h = 10 or b = 10, h = 4.

So, the altitude of the parallelogram can be either 10 m or 4 m.