If the area of a semi-circular region is 77 sq m, then its radius is……………………………

Answer

To find the radius of a semi-circular region given that its area is 77 sq m, we can follow these steps:

### Step-by-Step Solution:

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.

2. **Set up the equation**:
We know the area of the semicircle is 77 sq m. Therefore, we can set up the equation:
\[ \frac{1}{2} \pi r^2 = 77 \]

3. **Multiply both sides by 2**:
To eliminate the fraction, multiply both sides of the equation by 2:
\[ \pi r^2 = 154 \]

4. **Divide both sides by \( \pi \)**:
Next, divide both sides by \( \pi \) to isolate \( r^2 \):
\[ r^2 = \frac{154}{\pi} \]

5. **Substitute the value of \( \pi \)**:
Using \( \pi \approx \frac{22}{7} \), we can substitute this value into the equation:
\[ r^2 = \frac{154}{\frac{22}{7}} = 154 \times \frac{7}{22} \]

6. **Simplify the right side**:
Calculate \( 154 \times \frac{7}{22} \):
\[ r^2 = \frac{154 \times 7}{22} \]
First, simplify \( \frac{154}{22} \):
\[ \frac{154}{22} = 7 \quad (\text{since } 154 = 7 \times 22) \]
So,
\[ r^2 = 7 \times 7 = 49 \]

7. **Take the square root**:
To find \( r \), take the square root of both sides:
\[ r = \sqrt{49} = 7 \]

8. **State the final answer**:
Therefore, the radius of the semicircular region is:
\[ r = 7 \text{ m} \]