Identify the dimensions of rectangle ADEH.

The length $AD = 62 \text{ mm}$ and the width $AH = 32 \text{ mm}$.

The perimeter $P$ of a rectangle is given by $P = 2 \times (\text{length} + \text{width})$.

The perimeter of rectangle $ADEH$ is $\boxed{\text{188 mm}}$.

Since $ADEH$ is a rectangle, $DE = AH = 32 \text{ mm}$.
From the figure, $FE = 18 \text{ mm}$. Since $CDEF$ is a rectangle, $CD = FE = 18 \text{ mm}$.
So, the length $CD = 18 \text{ mm}$ and the width $DE = 32 \text{ mm}$.

The perimeter of rectangle $CDEF$ is $\boxed{\text{100 mm}}$.

The total length $HE = AD = 62 \text{ mm}$.
We know $HE = HG + GF + FE$.

The base of the triangle is $HF = HG + GF = 20 \text{ mm} + 24 \text{ mm} = 44 \text{ mm}$.
The height of the triangle is $BG$. Since $ADEH$ is a rectangle, $BG = AH = 32 \text{ mm}$.
The area $A$ of a triangle is given by $A = \frac{1}{2} \times \text{base} \times \text{height}$.

The length $CD = 18 \text{ mm}$ and the width $DE = 32 \text{ mm}$.
The area $A$ of a rectangle is given by $A = \text{length} \times \text{width}$.

The total shaded area is the sum of the area of triangle $HBF$ and the area of rectangle $CDEF$.

The area of the shaded region within rectangle $ADEH$ is $\boxed{\text{1280 mm}^2}$.