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.