Find the area (in `cm^(2)`) of a semi-circle of radius 14 cm.

Options

A. 308
B. 616
C. 160
D. 320

Answer

To find the area of a semi-circle with a radius of 14 cm, we can follow these steps:

### Step 1: Understand the formula for the area of a semi-circle
The area \( A \) of a semi-circle is given by the formula:
\[ A = \frac{1}{2} \pi r^2 \]
where \( r \) is the radius of the semi-circle.

### Step 2: Substitute the radius into the formula
Given that the radius \( r = 14 \) cm, we substitute this value into the formula:
\[ A = \frac{1}{2} \pi (14)^2 \]

### Step 3: Calculate \( r^2 \)
First, calculate \( 14^2 \):
\[ 14^2 = 196 \]

### Step 4: Substitute \( r^2 \) back into the area formula
Now substitute \( 196 \) back into the area formula:
\[ A = \frac{1}{2} \pi (196) \]

### Step 5: Use the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \), we can substitute this into the formula:
\[ A = \frac{1}{2} \times \frac{22}{7} \times 196 \]

### Step 6: Simplify the expression
Now, simplify the expression:
1. Calculate \( \frac{1}{2} \times 196 = 98 \)
2. Now multiply \( 98 \) by \( \frac{22}{7} \):
\[ A = 98 \times \frac{22}{7} \]

### Step 7: Perform the multiplication
To perform the multiplication:
\[ A = \frac{98 \times 22}{7} \]
Calculating \( 98 \times 22 = 2156 \), then divide by \( 7 \):
\[ A = \frac{2156}{7} = 308 \]

### Step 8: Final area result
Thus, the area of the semi-circle is:
\[ A = 308 \, \text{cm}^2 \]