To calculate the perimeter and area of this shape, I'll break down the analysis:

Step 1: Analyze the Shape

The given diagram shows a combination of a rectangle and a right-angled triangle on top of it. The dimensions provided are:

• Height of the entire figure: 17.8 cm.
• Width of the rectangle: 12.5 cm.

Step 2: Break Down the Shape

1. Rectangle:

   • Height = $h_1$ (unknown, the height of the rectangle).
   • Width = 12.5 cm.

2. Right-Angled Triangle (on top of the rectangle):

   • Base = 12.5 cm (same as the width of the rectangle).
   • Total height = 17.8 cm, so the height of the triangle = $17.8 \, \text{cm} - h_1$.

Step 3: Calculate the Perimeter

To calculate the perimeter, we need all sides:

1. The perimeter of the rectangle part = $2 \times (h_1 + 12.5 \, \text{cm})$.
2. The hypotenuse of the triangle can be found using the Pythagorean theorem: $\text{Hypotenuse} = \sqrt{(12.5)^2 + (17.8 - h_1)^2}$
3. Add up the sides to get the total perimeter.

Step 4: Calculate the Area

The total area is the sum of the areas of the rectangle and the triangle:

1. Area of the Rectangle: $\text{Area of Rectangle} = 12.5 \times h_1$
2. Area of the Triangle: $\text{Area of Triangle} = \frac{1}{2} \times 12.5 \times (17.8 - h_1)$
3. Total Area: $\text{Total Area} = (12.5 \times h_1) + \frac{1}{2} \times 12.5 \times (17.8 - h_1)$

Step 5: Estimation for Reasonableness

1. Consider the whole shape roughly as a rectangle with the dimensions 12.5 cm × 17.8 cm.
2. Approximate perimeter and area using those dimensions to ensure the calculated values make sense.

Would you like me to continue with the detailed calculations and determine $h_1$?