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To find the area of triangle \( ABC \) with sides \( AB = 11 \, \text{cm} \), \( BC = 7 \, \text{cm} \), and \( CA = 8 \, \text{cm} \), we can use **Heron's formula**.

### Step 1: Calculate the semi-perimeter \( s \)
The semi-perimeter \( s \) is given by:
\[
s = \frac{AB + BC + CA}{2} = \frac{11 + 7 + 8}{2} = \frac{26}{2} = 13 \, \text{cm}
\]

### Step 2: Use Heron's formula
The area \( A \) of the triangle is calculated using the formula:
\[
A = \sqrt{s(s - AB)(s - BC)(s - CA)}
\]
Substituting the values:
\[
A = \sqrt{13(13 - 11)(13 - 7)(13 - 8)}
\]
\[
A = \sqrt{13 \times 2 \times 6 \times 5}
\]
\[
A = \sqrt{13 \times 60} = \sqrt{780}
\]

### Step 3: Calculate the square root
\[
A \approx \sqrt{780} \approx 27.928
\]

### Step 4: Round to 3 significant figures
\[
\text{Area} \approx 27.9 \, \text{cm}^2
\]

### Final Answer
The area of triangle \( ABC \) is \( 27.9 \, \text{cm}^2 \) to 3 significant figures.

Would you like more details or have any questions?

Here are some related questions you might find useful:
1. How do you derive Heron's formula?
2. What are other methods to find the area of a triangle if angles are known?
3. Can you use trigonometric ratios to solve this triangle?
4. What is the significance of the semi-perimeter in Heron's formula?
5. How does Heron's formula apply to right-angled triangles?

**Tip:** When using Heron's formula, ensure you calculate the semi-perimeter accurately as it is crucial for determining the correct area.

In the triangle ABC, AB = 11 cm, BC = 7 cm, and CA = 8 cm. Find the area of triangle ABC, giving your answer in cm² to 3 significant figures.

Learn how to calculate the area of triangle ABC with sides AB = 11 cm, BC = 7 cm, and CA = 8 cm using Heron's formula. This problem involves applying geometry concepts and Heron's theorem, suitable for students in Grades 9-11. The final answer is approximately 27.9 cm².

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