The area of `triangleABC` is 8 `cm^(2)` in which AB=AC=4 cm and `angleA=90^(@)`.

Explanation

To solve the problem, we need to verify if the area of triangle ABC is indeed 8 cm² given that AB = AC = 4 cm and angle A = 90°.

### Step-by-Step Solution:

1. **Identify the Type of Triangle**:
- Since AB = AC and angle A = 90°, triangle ABC is an isosceles right triangle.

2. **Determine the Base and Height**:
- In a right triangle, we can consider one leg as the base and the other leg as the height. Here, we can take AB as the base and AC as the height. Thus:
- Base (AB) = 4 cm
- Height (AC) = 4 cm

3. **Use the Area Formula for a Triangle**:
- The formula for the area of a triangle is:
\[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]
- Substituting the values we have:
\[ \text{Area} = \frac{1}{2} \times 4 \times 4 \]

4. **Calculate the Area**:
- First, calculate \(4 \times 4\):
\[ 4 \times 4 = 16 \]
- Now, multiply by \(\frac{1}{2}\):
\[ \text{Area} = \frac{1}{2} \times 16 = 8 \text{ cm}^2 \]

5. **Conclusion**:
- The calculated area of triangle ABC is 8 cm², which matches the given area in the problem statement. Therefore, the statement is true.