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Question 3 shows a triangle \( ABC \) with the sides:

- \( AB = 10.4 \, \text{cm} \),
- \( AC = 11.0 \, \text{cm} \),
- \( BC = 9.7 \, \text{cm} \).

We are asked to find the area of the triangle to 3 significant figures.

### Using Heron's Formula:

The area \( A \) of a triangle given its sides \( a \), \( b \), and \( c \) can be calculated using Heron's formula:
\[
A = \sqrt{s(s - a)(s - b)(s - c)}
\]
where \( s \) is the semi-perimeter:
\[
s = \frac{a + b + c}{2}
\]

Here, \( a = 10.4 \, \text{cm} \), \( b = 11.0 \, \text{cm} \), and \( c = 9.7 \, \text{cm} \).

Let me calculate the area using these values.The area of triangle \( ABC \) is approximately \( 46.2 \, \text{cm}^2 \) to 3 significant figures.

Would you like more details, or do you have any other questions?

Here are 5 related questions:
1. How would you apply Heron's formula to a triangle with sides 7 cm, 8 cm, and 9 cm?
2. What is the significance of the semi-perimeter in Heron's formula?
3. Can you derive the area using the formula \( \frac{1}{2} \times \text{base} \times \text{height} \)?
4. How would you find the height of triangle ABC if you knew the area and base?
5. How does Heron's formula differ from using trigonometric methods to find the area of a triangle?

**Tip:** Always double-check side lengths and units when using Heron’s formula to avoid errors.

Find the area of triangle ABC with sides AB = 10.4 cm, AC = 11.0 cm, and BC = 9.7 cm using Heron's formula. A step-by-step solution for calculating the area to 3 significant figures, suitable for students in Grades 9-11.

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