https://file.aiquickdraw.com/mathbot/file/1725478241285gbxmf7fw.jpg

To solve the problem, let's first break down what is required:

### Problem Statement:
We need to find the perimeter of a minor sector of a circle with:
- **Radius (r)** = 4 units
- **Angle subtended at the center (θ)** = 45°

### Step 1: Formula for the Perimeter of a Sector
The perimeter of a sector is given by the formula:

\[
\text{Perimeter} = 2r + \text{Length of the arc}
\]

### Step 2: Calculate the Length of the Arc
The length of the arc \( L \) can be calculated using the formula:

\[
L = r \times \theta
\]

Where:
- \( r \) is the radius
- \( \theta \) is the angle in radians

Since the angle is given in degrees, convert it to radians:

\[
\theta = \frac{45^\circ \times \pi}{180^\circ} = \frac{\pi}{4} \text{ radians}
\]

Now calculate the arc length:

\[
L = 4 \times \frac{\pi}{4} = \pi \text{ units}
\]

### Step 3: Calculate the Perimeter
Using the perimeter formula:

\[
\text{Perimeter} = 2r + L = 2(4) + \pi = 8 + \pi \text{ units}
\]

### Answer:
The correct answer is **8 + π units**, which corresponds to option **3**.

Would you like further details on this, or do you have any additional questions?

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**Related Questions:**
1. How do you convert degrees to radians, and why is it necessary?
2. How would the perimeter change if the angle subtended was 60° instead of 45°?
3. What is the relationship between the radius and the arc length in a circle?
4. Can you derive the formula for the area of a sector and compare it with the perimeter?
5. What happens to the perimeter as the subtended angle approaches 360°?

**Tip:** Always ensure that the angle is in radians when using formulas involving trigonometric functions or arc length calculations.

The perimeter of a minor sector of a circle of radius 4 units subtending an angle of 45° is:

Calculate the perimeter of a minor sector of a circle with a radius of 4 units and an angle of 45°. This problem covers core geometric concepts including arc length, sector perimeter, and conversion between degrees and radians. Suitable for students in Grades 9-11.

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