To calculate the perimeter of the given shape, we need to add up the lengths of all its sides.

1. Given Information:

   • Straight sides: $4 \, \text{cm}, 4 \, \text{cm}, 7 \, \text{cm}, 5 \, \text{cm}$
   • A curved side: This is a circular arc of a sector.

2. Find the length of the arc: The length of an arc $L$ is given by: $L = r \theta$ where $r$ is the radius of the circle and $\theta$ is the angle in radians.

   • Radius $r = 4 \, \text{cm}$
   • Angle $\theta = 40^\circ = \frac{40 \pi}{180} \, \text{radians} = \frac{2\pi}{9} \, \text{radians}$

   Substituting into the formula: $L = 4 \times \frac{2\pi}{9} = \frac{8\pi}{9} \, \text{cm} \approx 2.79 \, \text{cm}$

3. Calculate the total perimeter: Add the straight sides and the arc length: $\text{Perimeter} = 4 + 4 + 7 + 5 + 2.79 = 22.79 \, \text{cm}$

Final Answer:

The perimeter of the shape is approximately 22.79 cm.

Would you like further clarification or assistance with similar problems? Here are some related questions for practice:

1. How do you calculate the area of the circular sector in this problem?
2. What is the total angle in radians for a complete circle?
3. How would the perimeter change if the angle were 60° instead of 40°?
4. Can the formula for arc length be used for any curve? Why or why not?
5. How is the radian measure related to degrees?

Tip: Always remember to convert angles to radians when using formulas involving circular motion or sectors!