To find the area of the triangle in the image, we can use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Here, the base of the triangle is given as $12 \, \text{cm}$ and the height (the perpendicular line) is $5 \, \text{cm}$.

Let's substitute these values into the formula:

$\text{Area} = \frac{1}{2} \times 12 \, \text{cm} \times 5 \, \text{cm} = \frac{1}{2} \times 60 \, \text{cm}^2 = 30 \, \text{cm}^2$

So, the area of the triangle is 30 cm².

Would you like any further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the area change if the base were doubled?
2. What happens to the area if the height is halved?
3. How do you find the area of triangles that don’t have a right angle?
4. Could you calculate the perimeter of this triangle?
5. What other formulas can be used to find the area of a triangle?

Tip: When calculating the area of a triangle, always ensure that the base and height are perpendicular to each other.