To find the area of a triangle with sides of lengths 10 cm, 24 cm, and 26 cm, we can use Heron's Formula. The formula for the area $A$ of a triangle is:

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

Where:

• $a = 10 \, \text{cm}$
• $b = 24 \, \text{cm}$
• $c = 26 \, \text{cm}$
• $s$ is the semi-perimeter, calculated as:

$s = \frac{a + b + c}{2}$

Let's compute this step by step:

1. Calculate the semi-perimeter $s$:

$s = \frac{10 + 24 + 26}{2} = \frac{60}{2} = 30$

2. Apply Heron's formula:

$A = \sqrt{30(30 - 10)(30 - 24)(30 - 26)}$ $A = \sqrt{30(20)(6)(4)}$ $A = \sqrt{30 \times 480}$ $A = \sqrt{14400}$ $A = 120 \, \text{cm}^2$

So, the area of the triangle is 120 cm².

Would you like further explanation or details on any of the steps?

Here are 5 related questions:

1. How do you use Heron's formula for other types of triangles?
2. What happens if the triangle is a right triangle? Can you calculate the area differently?
3. What is the relationship between the sides of a right triangle and the area?
4. How do you calculate the area of a triangle when only the base and height are known?
5. Can you derive Heron’s formula starting from basic principles?

Tip: When using Heron's formula, ensure that the triangle is valid (i.e., the sum of any two sides must be greater than the third side).