Math worksheet for calculating the perimeter and area of semicircles and quadrants, featuring various geometric shapes with given dimensions.

Absolutely! Let’s solve each part step by step. The worksheet asks for the perimeter and area of semicircles (half-circles) and quadrants (quarter-circles), using π = 3.142, and rounding answers to 1 decimal place.

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## 🔷 Key Formulas:

For a Semicircle:

- Perimeter = Half the circumference + diameter
→ `P = (π × r) + 2r` or `P = π × r + d` (since d = 2r)
- Area = Half the area of a full circle
→ `A = (π × r²) / 2`

For a Quadrant (Quarter Circle):

- Perimeter = Quarter of circumference + 2 radii (the two straight sides)
→ `P = (π × r)/2 + 2r`
- Area = Quarter of the area of a full circle
→ `A = (π × r²) / 4`

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Now let’s solve each one:

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a) Semicircle, radius = 3 cm

- Perimeter = πr + 2r = (3.142 × 3) + (2 × 3) = 9.426 + 6 = 15.4 cm
- Area = (π × r²)/2 = (3.142 × 9)/2 = 28.278 / 2 = 14.1 cm²

✔ Answer: Perimeter = 15.4 cm, Area = 14.1 cm²

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b) Semicircle, radius = 4 cm

- Perimeter = πr + 2r = (3.142 × 4) + 8 = 12.568 + 8 = 20.6 cm
- Area = (π × 16)/2 = (50.272)/2 = 25.1 cm²

✔ Answer: Perimeter = 20.6 cm, Area = 25.1 cm²

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c) Semicircle, diameter = 6 cm → so radius = 3 cm

*(Same as part a!)*

- Perimeter = πr + 2r = (3.142 × 3) + 6 = 9.426 + 6 = 15.4 cm
- Area = (π × 9)/2 = 28.278 / 2 = 14.1 cm²

✔ Answer: Perimeter = 15.4 cm, Area = 14.1 cm²

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d) Semicircle, diameter = 3.5 cm → radius = 1.75 cm

- Perimeter = πr + 2r = (3.142 × 1.75) + 3.5 = 5.4985 + 3.5 = 9.0 cm (rounded to 1 dp)
- Area = (π × r²)/2 = (3.142 × 3.0625)/2 = 9.621 / 2 = 4.8 cm²

✔ Answer: Perimeter = 9.0 cm, Area = 4.8 cm²

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e) Quadrant, radius = 2 mm

- Perimeter = (πr)/2 + 2r = (3.142 × 2)/2 + 4 = 3.142 + 4 = 7.1 mm
- Area = (π × r²)/4 = (3.142 × 4)/4 = 12.568 / 4 = 3.1 mm²

✔ Answer: Perimeter = 7.1 mm, Area = 3.1 mm²

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f) Quadrant, radius = 1.5 m

- Perimeter = (π × 1.5)/2 + 3 = (4.713)/2 + 3 = 2.3565 + 3 = 5.4 m
- Area = (π × 2.25)/4 = (7.0695)/4 = 1.8 m²

✔ Answer: Perimeter = 5.4 m, Area = 1.8 m²

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g) Quadrant, radius = 7 m

- Perimeter = (π × 7)/2 + 14 = (21.994)/2 + 14 = 10.997 + 14 = 25.0 m
- Area = (π × 49)/4 = (153.958)/4 = 38.5 m²

✔ Answer: Perimeter = 25.0 m, Area = 38.5 m²

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h) Quadrant, radius = 13 m

- Perimeter = (π × 13)/2 + 26 = (40.846)/2 + 26 = 20.423 + 26 = 46.4 m
- Area = (π × 169)/4 = (530.938)/4 = 132.7 m²

✔ Answer: Perimeter = 46.4 m, Area = 132.7 m²

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## ✔ Final Answers Summary:

| Part | Perimeter | Area |
|------|------------------|---------------|
| a) | 15.4 cm | 14.1 cm² |
| b) | 20.6 cm | 25.1 cm² |
| c) | 15.4 cm | 14.1 cm² |
| d) | 9.0 cm | 4.8 cm² |
| e) | 7.1 mm | 3.1 mm² |
| f) | 5.4 m | 1.8 m² |
| g) | 25.0 m | 38.5 m² |
| h) | 46.4 m | 132.7 m² |

Let me know if you’d like a diagram explanation or step-by-step calculations for any specific part!