To calculate the area of a semi-circle with a given diameter, follow these steps:
1. Understand the given information:
- Diameter of the semi-circle: 14 cm
- Value of π (pi) to use: [tex]\(\frac{22}{7}\)[/tex]
2. Calculate the radius of the semi-circle:
- The radius (r) is half of the diameter.
[tex]\[ r = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \text{ cm} \][/tex]
3. Recall the formula for the area of a full circle:
- The area (A) of a full circle is given by:
[tex]\[ A_{\text{full}} = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
4. Calculate the area of the full circle with the given radius:
[tex]\[ A_{\text{full}} = \left(\frac{22}{7}\right) \times (7)^2 \][/tex]
[tex]\[ A_{\text{full}} = \left(\frac{22}{7}\right) \times 49 \][/tex]
[tex]\[ A_{\text{full}} = 22 \times 7 \][/tex]
[tex]\[ A_{\text{full}} = 154 \text{ cm}^2 \][/tex]
5. Determine the area of the semi-circle:
- The area of the semi-circle is half the area of the full circle.
[tex]\[ A_{\text{semi}} = \frac{A_{\text{full}}}{2} = \frac{154}{2} = 77 \text{ cm}^2 \][/tex]
So, the area of the semi-circle whose diameter is 14 cm is [tex]\( 77 \text{ cm}^2 \)[/tex].
