The inradius and circumradius of a right angle triangle are 6 cm and 16 cm. Find the area ((insq.cm) of the triangle.

Options

A. A)304
B. B)228
C. C)288
D. D)none of these

Answer

To find the area of the right-angled triangle given its inradius (r) and circumradius (R), we can use the formula for the area of a triangle in terms of its inradius and circumradius:

\[ \text{Area} = r \times (r + 2R) \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Inradius (r) = 6 cm
- Circumradius (R) = 16 cm

2. **Substitute the values into the area formula:**
\[ \text{Area} = r \times (r + 2R) \]
\[ \text{Area} = 6 \times (6 + 2 \times 16) \]

3. **Calculate the expression inside the parentheses:**
- First, calculate \(2 \times 16\):
\[ 2 \times 16 = 32 \]
- Now add this to \(r\):
\[ 6 + 32 = 38 \]

4. **Multiply by the inradius:**
\[ \text{Area} = 6 \times 38 \]

5. **Perform the multiplication:**
\[ 6 \times 38 = 228 \]

6. **Final result:**
The area of the triangle is \(228 \, \text{cm}^2\).

### Conclusion:
The area of the triangle is \(228 \, \text{cm}^2\).

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