The area of a semicircle is `308 cm^(2)`. Find its perimeter

Answer

To find the perimeter of a semicircle given its area, we can follow these steps:

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

### Step 2: Set up the equation with the given area.
We are given that the area of the semicircle is \( 308 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ \frac{1}{2} \pi r^2 = 308 \]

### Step 3: Substitute the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \), we can substitute this value into the equation:
\[ \frac{1}{2} \times \frac{22}{7} \times r^2 = 308 \]

### Step 4: Simplify the equation.
Multiplying both sides by 2 to eliminate the fraction gives:
\[ \frac{22}{7} r^2 = 616 \]
Now, multiply both sides by \( 7 \):
\[ 22 r^2 = 616 \times 7 \]
Calculating \( 616 \times 7 \):
\[ 22 r^2 = 4312 \]

### Step 5: Solve for \( r^2 \).
Now divide both sides by \( 22 \):
\[ r^2 = \frac{4312}{22} \]
Calculating this gives:
\[ r^2 = 196 \]

### Step 6: Find the radius \( r \).
Taking the square root of both sides:
\[ r = \sqrt{196} = 14 \, \text{cm} \]

### Step 7: Calculate the perimeter of the semicircle.
The perimeter \( P \) of a semicircle is given by the formula:
\[ P = \pi r + 2r \]
Substituting the value of \( r \) and \( \pi \):
\[ P = \frac{22}{7} \times 14 + 2 \times 14 \]

### Step 8: Simplify the perimeter calculation.
Calculating \( \frac{22}{7} \times 14 \):
\[ \frac{22 \times 14}{7} = 44 \]
Calculating \( 2 \times 14 \):
\[ 2 \times 14 = 28 \]
Now, adding these two results:
\[ P = 44 + 28 = 72 \, \text{cm} \]

### Final Answer:
The perimeter of the semicircle is \( 72 \, \text{cm} \).

---