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can you find the Formula to calculate perimeter of each shape

The image shows three distinct geometric shapes: a circle with a sector, a trapezoid, and a smaller circle. I'll outline the formulas needed to calculate the perimeter of each of these shapes based on the given dimensions.

### 1. **Perimeter of the Yellow Circle with a Sector:**
The perimeter of a circle with a sector consists of the arc length and the two radii of the sector.

- **Radius (R)** = 6 cm
- **Sector Angle (θ)** = 295° (convert to radians for formulas, or use degrees in sector-specific formulas)

**Formula:**
\[
\text{Perimeter of the sector} = 2R + \text{Arc Length}
\]
where:
\[
\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi R
\]

Substitute the values for \( R = 6 \, \text{cm} \) and \( \theta = 295^\circ \) to find the perimeter.

### 2. **Perimeter of the Trapezoid:**
The trapezoid has four sides of different lengths:
- **Top side (a)** = 8 cm
- **Bottom side (b)** = 14 cm
- **Left diagonal side** = 7 cm
- **Right diagonal side** = 7.6 cm

**Formula:**
\[
\text{Perimeter of the trapezoid} = a + b + \text{left side} + \text{right side}
\]
Substitute the known side lengths to find the perimeter.

### 3. **Perimeter of the Small Blue Circle:**
For a circle, the perimeter is the circumference. The diameter is twice the radius.

- **Radius (r)** = 2.5 cm

**Formula:**
\[
\text{Perimeter (Circumference) of the circle} = 2\pi r
\]
Substitute \( r = 2.5 \, \text{cm} \) to calculate the perimeter of the small circle.

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Would you like me to calculate these values for you? Let me know if you have any further questions.

### Relative Questions:
1. How do you calculate the arc length for a sector with different angles?
2. What is the significance of converting degrees to radians in sector calculations?
3. What is the perimeter formula for a general polygon?
4. How do diagonal sides of a trapezoid affect its perimeter?
5. What is the formula for the perimeter of an ellipse?

### Tip:
Always ensure you have consistent units across all measurements before calculating perimeters or areas for any composite shape.

Can you find the Formula to calculate the perimeter of each shape?

Learn how to calculate the perimeter of a sector of a circle, a trapezoid, and a small circle using geometric formulas. Includes step-by-step formulas for arc length, trapezoid side lengths, and circle circumference, with real-life application examples. Suitable for students in Grades 8-10.

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