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

Answer

To solve the problem, we need to find the perimeter of a semicircle given its area. Here’s a step-by-step solution:

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

### Step 2: Set up the equation using the given area
We know 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: Solve for \( r^2 \)
To isolate \( r^2 \), we first multiply both sides by 2:
\[ \pi r^2 = 616 \]
Next, we divide both sides by \( \pi \):
\[ r^2 = \frac{616}{\pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ r^2 = \frac{616 \times 7}{22} = \frac{4312}{22} = 196 \]

### Step 4: Calculate the radius \( r \)
Now, we take the square root of both sides to find \( r \):
\[ r = \sqrt{196} = 14 \, \text{cm} \]

### Step 5: Calculate the perimeter of the semicircle
The perimeter \( P \) of a semicircle is given by the formula:
\[ P = \pi r + 2r \]
Substituting \( r = 14 \, \text{cm} \):
\[ P = \pi \times 14 + 2 \times 14 \]
Using \( \pi \approx \frac{22}{7} \):
\[ P = \frac{22}{7} \times 14 + 28 \]
Calculating \( \frac{22}{7} \times 14 \):
\[ P = 44 + 28 = 72 \, \text{cm} \]

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

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