To find the perimeter of a semi-circle, you need to consider both the curved part of the semi-circle and the diameter (straight line across).
- First, find the curved part of the semi-circle. The formula for the circumference of a full circle is: \(C = 2\pi r\) Given that the radius \(r = 21 \text{ cm}\) and \(\pi = \frac{22}{7}\), the circumference of the full circle would be: \(C = 2 \times \frac{22}{7} \times 21\).
- Simplify the calculation:
- First, multiply: \(2 \times 21 = 42\)
- Then multiply by \(\frac{22}{7}\): \(42 \times \frac{22}{7} = 132\)
- The length of the curved part of the semi-circle is half of the full circumference: \(\frac{132}{2} = 66 \text{ cm}\).
- The diameter of the circle also forms part of the semi-circle perimeter. This is twice the radius: \(D = 2 \times 21 = 42 \text{ cm}\).
- Add the curved part and the diameter to find the total perimeter of the semi-circle: \(66 + 42 = 108 \text{ cm}\).
Thus, the perimeter of the semi-circle is 108 cm, which is the correct answer.