Let’s analyze the problem and solve it step by step.

Problem Description:

• The shape is a combination of a rectangle and three-quarters of a circle.
• The rectangle's dimensions are 4 m (length) and 3 m (height).
• The circle's radius is 2 m, and the circle is positioned so that three-quarters of its perimeter forms part of the shape.

We are tasked with finding the perimeter of the shape to two decimal places, and π is approximated as 3.14.

Solution:

Step 1: Perimeter of the rectangle

The perimeter of the rectangle includes:

• Two full sides (3 m and 4 m), and
• Two other sides, where part of the circle replaces one corner.

Thus, the linear part of the rectangle in the perimeter is: $4 \, \text{m (bottom)} + 3 \, \text{m (right)} = 7 \, \text{m}.$

Step 2: Three-quarters of the circle's circumference

The circle's radius is $r = 2 \, \text{m}$. The circumference of the full circle is: $C = 2 \pi r = 2 \times 3.14 \times 2 = 12.56 \, \text{m}.$

Since only three-quarters of the circle is part of the perimeter, we calculate: $\text{Three-quarters of the circumference} = \frac{3}{4} \times 12.56 = 9.42 \, \text{m}.$

Step 3: Total Perimeter

The total perimeter is the sum of the linear part of the rectangle and the three-quarters of the circle: $\text{Perimeter} = 7 + 9.42 = 16.42 \, \text{m}.$

Final Answer:

The perimeter of the shape is: $\boxed{16.42 \, \text{m}}$

Let me know if you'd like more details or have further questions. Below are some related questions to expand your understanding:

1. How would the perimeter change if the circle were a full circle instead of three-quarters?
2. How is the area of the shape calculated?
3. What if the rectangle’s dimensions were different? How would that affect the perimeter?
4. What happens to the calculation if π is used as 3.14159 instead of 3.14?
5. How do you calculate the arc length for any fraction of a circle?

Tip: Always break down composite shapes into their basic components to simplify calculations.