The problem involves determining both the perimeter and the area of a composite shape made of part of a circle and a rectangle. Let’s analyze and solve the problem step by step.

Observations:

1. The shape includes:

   • A rectangle.
   • A semicircle attached to one side of the rectangle.

2. The dimensions visible in the image:

   • The width of the rectangle (and the diameter of the semicircle) is 4 units.
   • The height of the rectangle is 3 units.

3. The radius of the semicircle can be deduced:

   • Radius $r = \frac{\text{Diameter}}{2} = \frac{4}{2} = 2 \, \text{units}$.

(a) Perimeter of the Shape

The perimeter includes:

1. The two vertical sides of the rectangle: $2 \times 3 = 6 \, \text{units}$.
2. The curved part of the semicircle (half the circumference of a full circle):
   $\text{Semicircle arc} = \frac{1}{2} \times 2 \pi r = \pi r = \pi \times 2 = 2\pi \, \text{units}.$

Thus, the total perimeter: $P = 6 + 2\pi \approx 6 + 6.28 = 12.28 \, \text{units}.$

(b) Area of the Shape

The total area is the sum of:

1. The area of the rectangle:
   $\text{Rectangle area} = \text{width} \times \text{height} = 4 \times 3 = 12 \, \text{square units}.$

2. The area of the semicircle:
   $\text{Semicircle area} = \frac{1}{2} \times \pi r^2 = \frac{1}{2} \pi (2^2) = \frac{1}{2} \pi (4) = 2\pi \, \text{square units}.$

Thus, the total area: $A = 12 + 2\pi \approx 12 + 6.28 = 18.28 \, \text{square units}.$

Final Answers:

(a) Perimeter: $\approx 12.28 \, \text{units}$.
(b) Area: $\approx 18.28 \, \text{square units}$.

Would you like a step-by-step visual breakdown or further clarifications?

5 Related Questions:

1. How does the formula for the circumference of a circle help in perimeter calculations for semicircles?
2. What would happen to the perimeter and area if the semicircle were replaced by a full circle?
3. How do we approximate $\pi$ when solving problems involving circles?
4. How can composite shapes be divided to simplify area calculations?
5. What is the difference between perimeter and circumference?

Tip:

Always ensure dimensions are in the same units before performing calculations in geometry.