Find the area (in `cm^(2)`) of a semicircle of radius 21 cm.

Options

A. 1386
B. 960
C. 693
D. 1920

Answer

To find the area of a semicircle with a radius of 21 cm, we can follow these steps:

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

### Step 2: Determine the area of the semicircle.
Since we are looking for the area of a semicircle, we take half of the area of the full circle:
\[ \text{Area of semicircle} = \frac{1}{2} \times \pi r^2 \]

### Step 3: Substitute the radius into the formula.
Given that the radius \( r = 21 \) cm, we substitute this value into the formula:
\[ \text{Area of semicircle} = \frac{1}{2} \times \pi \times (21)^2 \]

### Step 4: Calculate \( (21)^2 \).
First, calculate \( 21^2 \):
\[ 21^2 = 441 \]

### Step 5: Substitute \( 441 \) back into the formula.
Now, substitute \( 441 \) back into the area formula:
\[ \text{Area of semicircle} = \frac{1}{2} \times \pi \times 441 \]

### Step 6: Use the value of \( \pi \).
For this calculation, we can use \( \pi \approx \frac{22}{7} \):
\[ \text{Area of semicircle} = \frac{1}{2} \times \frac{22}{7} \times 441 \]

### Step 7: Simplify the expression.
Now, simplify the expression:
\[ \text{Area of semicircle} = \frac{22 \times 441}{14} \]

### Step 8: Calculate \( 22 \times 441 \).
Now calculate \( 22 \times 441 \):
\[ 22 \times 441 = 9702 \]

### Step 9: Divide by 14.
Now divide \( 9702 \) by \( 14 \):
\[ \text{Area of semicircle} = \frac{9702}{14} = 693 \]

### Final Answer:
Thus, the area of the semicircle is:
\[ \text{Area} = 693 \, \text{cm}^2 \]

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