A paper is in the form of a rectangle ABCD where AB = 21 cm and BC = 14 cm. A semicircular portion with BC as diameter is cut off. Find the area of the remaining paper

Answer

To find the area of the remaining paper after cutting off a semicircular portion from a rectangular sheet, we can follow these steps:

### Step-by-Step Solution

1. **Identify the dimensions of the rectangle:**
- Given: Length (AB) = 21 cm and Width (BC) = 14 cm.

2. **Calculate the area of the rectangle (A):**
\[ \text{Area of rectangle} = \text{Length} \times \text{Width} = AB \times BC = 21 \, \text{cm} \times 14 \, \text{cm} \]
\[ A = 294 \, \text{cm}^2 \]

3. **Determine the diameter of the semicircle:**
- The diameter of the semicircle is equal to BC, which is 14 cm.

4. **Calculate the radius (r) of the semicircle:**
\[ r = \frac{\text{Diameter}}{2} = \frac{14 \, \text{cm}}{2} = 7 \, \text{cm} \]

5. **Calculate the area of the semicircle (A1):**
\[ \text{Area of semicircle} = \frac{\pi r^2}{2} \]
Using \(\pi \approx \frac{22}{7}\):
\[ A1 = \frac{22}{7} \times \frac{7 \times 7}{2} = \frac{22 \times 49}{14} = \frac{1078}{14} = 77 \, \text{cm}^2 \]

6. **Calculate the area of the remaining paper (A2):**
\[ A2 = A - A1 = 294 \, \text{cm}^2 - 77 \, \text{cm}^2 = 217 \, \text{cm}^2 \]

### Final Answer
The area of the remaining paper is \( 217 \, \text{cm}^2 \).

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