Let's break this problem down step by step:

Given:

• PQRS is a square.
• PQ = 14 cm (Side length of the square).
• PA = QB = RC = SD = 6 cm (Lengths of the segments from the vertices of the square to the points A, B, C, and D, respectively).

The goal is to find the perimeter of quadrilateral ABCD.

Step-by-Step Solution:

1. Side Length of Square: Since PQ = 14 cm, the side of the square PQRS is 14 cm.

2. Points A, B, C, and D:

   • Point A lies on side PQ such that PA = 6 cm. Therefore, AQ = PQ - PA = 14 - 6 = 8 cm.
   • Point B lies on side QR such that QB = 6 cm. Therefore, BR = QR - QB = 14 - 6 = 8 cm.
   • Point C lies on side RS such that RC = 6 cm. Therefore, CS = RS - RC = 14 - 6 = 8 cm.
   • Point D lies on side SP such that SD = 6 cm. Therefore, DP = SP - SD = 14 - 6 = 8 cm.

3. Perimeter of Quadrilateral ABCD: To find the perimeter of ABCD, we need to add the lengths of the sides AB, BC, CD, and DA.

   • AB = AQ + QB = 8 + 6 = 14 cm
   • BC = BR + RC = 8 + 6 = 14 cm
   • CD = CS + SD = 8 + 6 = 14 cm
   • DA = DP + PA = 8 + 6 = 14 cm

4. Total Perimeter: The perimeter of quadrilateral ABCD is the sum of these four sides:

   $\text{Perimeter} = AB + BC + CD + DA = 14 + 14 + 14 + 14 = 56 \, \text{cm}$

Thus, the perimeter of quadrilateral ABCD is 56 cm.

Final Answer:

The correct answer is (d) 56 cm.

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Would you like further clarification on any steps? Here are some related questions to explore:

1. How do you calculate the perimeter of a square?
2. How would the perimeter change if the segments PA, QB, RC, and SD were different?
3. Can you explain how to find the perimeter of polygons with irregular sides?
4. What is the relationship between the sides of a square and its diagonals?
5. How would you calculate the area of quadrilateral ABCD?

Tip: In geometric problems, always start by identifying the known measurements and relationships. This helps in breaking down the problem into manageable steps!