The problem asks us to determine the correct perimeter of the composite shape consisting of two semicircles and a rectangle. Here's the step-by-step breakdown:

Step 1: Analyze the Shape

• The composite shape consists of:
  • A rectangle with height $10$ (as labeled) and width $10$ (derived from the semicircles' radii since they are congruent).
  • Two semicircles with radius $r = 10$. Together, they form a complete circle.

Step 2: Calculate Perimeter Components

1. Rectangle's Perimeter Contribution:

   • The rectangle contributes two sides of $10 + 10 = 20$, since only its two vertical edges are included in the perimeter.

2. Circle's Perimeter Contribution:

   • The two semicircles form one full circle. The circumference of the full circle is: $2\pi r = 2\pi(10) = 20\pi$

3. Total Perimeter:

   • Add the contributions from the rectangle and the circle: $\text{Perimeter} = 20 + 20\pi$

Step 3: Match with Options

From the given choices:

• Correct Answers:
  • Option A: $40 + 20\pi$
  • Option B: $80 + 20\pi$ (if misreading the base).

Does this help? Or would you like a detailed breakdown?

Expanded Questions

1. Why does (20π) symbolize total arc total in circumference calculation?