**The terga, sterna, and pleura of a cockroach's body are joined by arthrodial membrane.**

The body of a cockroach is protected by a hard exoskeleton composed of several plates. These plates are known as terga, sterna, and pleura. The terga refers to the dorsal plates, sterna refers to the ventral plates, and pleura refers to the lateral plates of the cockroach's body.

**Arthrodial Membrane:**

The terga, sterna, and pleura are joined together by a flexible and elastic membrane known as the arthrodial membrane. This membrane allows for movement and flexibility in the cockroach's body. It is composed of a thin, flexible layer of cuticle that is reinforced by protein fibers. The arthrodial membrane acts as a hinge, allowing the terga, sterna, and pleura to move relative to each other.

**Function of Arthrodial Membrane:**

1. **Flexibility:** The arthrodial membrane allows for flexibility and movement between the terga, sterna, and pleura. This is essential for the cockroach's locomotion and various body movements.

2. **Protection:** The arthrodial membrane helps to protect the internal organs of the cockroach by providing support and stability to the exoskeleton. It acts as a barrier against physical damage and external threats.

3. **Joint Movement:** The arthrodial membrane enables the joints between the terga, sterna, and pleura to move in a controlled manner. This allows the cockroach to perform various activities such as walking, flying, and grooming.

4. **Elasticity:** The arthrodial membrane possesses elasticity, which allows it to return to its original shape after deformation. This elasticity ensures that the cockroach's body remains structurally sound and can withstand external forces.

In conclusion, the terga, sterna, and pleura of a cockroach's body are joined by an arthrodial membrane. This membrane provides flexibility, protection, joint movement, and elasticity, allowing the cockroach to carry out its essential activities and maintain its structural integrity.