To calculate the perimeter of the given L-shaped figure, let's proceed step-by-step.

Step 1: Identify the missing side

From the diagram:

• The vertical total height is 14 cm.
• On the right side:
  • Top vertical segment = 8 cm
  • Bottom vertical segment = missing side length.

To find the missing vertical side:

$\text{Missing side} = \text{Total height} - \text{Top segment}$ $\text{Missing side} = 14 \, \text{cm} - 8 \, \text{cm} = 6 \, \text{cm}.$

Step 2: Label all sides

Now the lengths of all sides are:

• Top horizontal: 5 cm
• Top-right vertical: 8 cm
• Bottom-right horizontal: 4 cm
• Missing vertical (bottom): 6 cm
• Bottom horizontal: 9 cm
• Left vertical: 14 cm

Step 3: Perimeter Calculation

The perimeter is the sum of all the outer edges. Add all the side lengths:

$P = 5 \, \text{cm} + 8 \, \text{cm} + 4 \, \text{cm} + 6 \, \text{cm} + 9 \, \text{cm} + 14 \, \text{cm}.$

$P = 46 \, \text{cm}.$

Final Answer:

The perimeter of the shape is 46 cm.

Would you like me to explain any part of this process further?

Related Questions:

1. How do you calculate the area of this L-shaped figure?
2. How do we confirm the perimeter using coordinates and distance formulas?
3. If the shape was scaled up by a factor of 2, what would be the new perimeter?
4. Can you determine the perimeter of a rectangle using the same total width and height?
5. How do we calculate the diagonal of a rectangular section in this figure?

Tip: Always double-check that you account for all sides, especially when working with composite shapes like L-shapes.