To find the area of a triangle with sides of 4 cm, 4 cm, and 6 cm, we can apply **Heron's formula**.

### Steps:
1. First, calculate the semi-perimeter \( s \):
   \[
   s = \frac{a + b + c}{2} = \frac{4 + 4 + 6}{2} = 7 \, \text{cm}
   \]
   where \( a = 4 \, \text{cm}, b = 4 \, \text{cm}, c = 6 \, \text{cm} \).

2. Then, use Heron's formula to find the area \( A \):
   \[
   A = \sqrt{s(s-a)(s-b)(s-c)}
   \]
   Substituting the values:
   \[
   A = \sqrt{7(7-4)(7-4)(7-6)} = \sqrt{7(3)(3)(1)}
   \]
   \[
   A = \sqrt{7 \times 9} = \sqrt{63} \approx 7.94 \, \text{cm}^2
   \]

So, the area of the triangle is approximately **7.94 cm²**.

Would you like more details or have any questions? 

Here are some related questions for further exploration:
1. How does Heron's formula work for all types of triangles?
2. What are the properties of an isosceles triangle?
3. Can Heron's formula be applied to a right triangle?
4. How do you derive Heron's formula?
5. How does changing one side affect the area of the triangle?

**Tip:** Always ensure you check if the triangle's side lengths satisfy the triangle inequality before applying any area formulas.

Learn how to calculate the area of an isosceles triangle with sides 4 cm, 4 cm, and 6 cm using Heron's formula. This detailed solution covers key geometric concepts and includes step-by-step instructions. Suitable for students in Grades 9-10.

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