The radius of in-circle of a triangle is 4 cm and the perimeter of the triangle is 20 cm. What is the area of the triangle?

Options

A. 40 sq. cm
B. 36 sq. cm
C. 80 sq. cm
D. 20 sq. cm

Answer

To find the area of the triangle given the radius of the in-circle (r) and the perimeter (P), we can use the formula that relates these quantities:

1. **Identify the given values**:
- Radius of the in-circle (r) = 4 cm
- Perimeter of the triangle (P) = 20 cm

2. **Calculate the semi-perimeter (s)**:
- The semi-perimeter (s) is half of the perimeter.
\[ s = \frac{P}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm} \]

3. **Use the formula for the area of the triangle**:
- The area (A) of a triangle can be calculated using the formula:
\[ A = r \times s \]
where r is the radius of the in-circle and s is the semi-perimeter.

4. **Substitute the values into the formula**:
\[ A = 4 \text{ cm} \times 10 \text{ cm} = 40 \text{ cm}^2 \]

5. **Conclusion**:
- The area of the triangle is \( 40 \text{ cm}^2 \).