https://file.aiquickdraw.com/mathbot/file/17255810825296ld6qbu0.jpg

The image contains three right-angled triangles, each with given side lengths, and the task is to determine the areas of these triangles. Here are the steps for calculating the area of a right-angled triangle:

The area \(A\) of a right-angled triangle can be calculated using the formula:

\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

### 1. Triangle 1:
- **Base** = 12 cm
- **Height** = 8 cm

\[
A = \frac{1}{2} \times 12 \times 8 = 48 \, \text{cm}^2
\]

### 2. Triangle 2:
- **Base** = 12 cm
- **Height** = 10 cm

\[
A = \frac{1}{2} \times 12 \times 10 = 60 \, \text{cm}^2
\]

### 3. Triangle 3:
- **Base** = 5 cm
- **Height** = 10 cm

\[
A = \frac{1}{2} \times 5 \times 10 = 25 \, \text{cm}^2
\]

### Summary of Results:
1. Area of Triangle 1: \(48 \, \text{cm}^2\)
2. Area of Triangle 2: \(60 \, \text{cm}^2\)
3. Area of Triangle 3: \(25 \, \text{cm}^2\)

Would you like a detailed explanation of any specific calculation or have any questions?

### Related Questions:
1. How do you find the perimeter of these triangles?
2. What is the hypotenuse of each triangle using the Pythagorean theorem?
3. How would you find the area of a non-right-angled triangle?
4. How can you apply trigonometric ratios to find unknown sides or angles?
5. How does the area formula change for different types of triangles?

### Tip:
For any right-angled triangle, remember that the base and height are always the two sides that form the right angle.

Determine the area of the right-angled triangles with given side lengths.

Learn how to calculate the area of three right-angled triangles with specific side lengths. This problem demonstrates how to use the formula A = 1/2 * base * height. Suitable for Grades 6-8 geometry students.

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