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To calculate the area of the triangle, we can use **Heron's formula** since we know the lengths of all three sides of the triangle. The sides of the triangle are given as:

- \( a = 7 \, \text{cm} \)
- \( b = 8 \, \text{cm} \)
- \( c = 10 \, \text{cm} \)

### Step 1: Calculate the semi-perimeter (\(s\)):
The semi-perimeter is half of the triangle's perimeter, calculated as:

\[
s = \frac{a + b + c}{2} = \frac{7 + 8 + 10}{2} = 12.5 \, \text{cm}
\]

### Step 2: Apply Heron's formula:
Heron's formula for the area \(A\) of a triangle is:

\[
A = \sqrt{s(s - a)(s - b)(s - c)}
\]

Substitute the values of \(s\), \(a\), \(b\), and \(c\):

\[
A = \sqrt{12.5(12.5 - 7)(12.5 - 8)(12.5 - 10)}
\]
\[
A = \sqrt{12.5(5.5)(4.5)(2.5)}
\]

I'll now calculate the exact area.The area of the triangle is approximately **27.81 cm²**.

Would you like more details or have any further questions? Here are five related questions you may find interesting:

1. How does Heron's formula apply to different types of triangles?
2. What are other methods for calculating the area of a triangle besides Heron's formula?
3. Can we always use Heron's formula, or are there cases where it's not applicable?
4. How do we calculate the area of a right triangle using simpler formulas?
5. What is the relationship between the semi-perimeter and the perimeter of any polygon?

**Tip:** Always check if a triangle is right-angled. If so, using simpler formulas like \(\frac{1}{2} \times \text{base} \times \text{height}\) can save time!

Calculate the area (in cm²) of the triangle with sides 7 cm, 8 cm, and 10 cm.

Learn how to calculate the area of a triangle using Heron's formula. This problem involves a triangle with side lengths of 7 cm, 8 cm, and 10 cm. Suitable for students in Grades 8-10.

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